The development of enterprises is faced with the repeated process of growth, maturity and decline. There are many complicated causes of decline and the strategies adopted by declining enterprises often determine their survival and sustainable development. Whether to give up or to seek new development opportunities is the confusion and strategic challenge faced by enterprise managers. Decline is defined as the continuous deterioration of the performance or resources of the enterprise over a period of time (Trahms et al., 2013). It is bound to weaken the competitiveness of enterprises and hamper their sustainable development. If the appropriate recovery strategy is not adopted in time, it is highly possible that circumstances might lead to the death of enterprises. Nowadays, under the background of big data, the applications of artificial intelligence and Internet of Things, enterprises are facing the most complex and confusing environment ever, which could increase all kinds of uncertainty and risks. It is an unavoidable fact that enterprises encounter with decline in business activities.
    In view of the continuous threat of decline, how to reverse the decline to achieve recovery is still a highly concerned and urgent problem to be solved by business managers. Relevant scholars call for innovation as a solution for declining enterprises (Wiseman & Bromiley, 1996; Mone et al., 1998; Greve, 2003; Audia & Greve, 2006; McKinley et al., 2014). But does decline promote innovation or produce rigidity to restrain innovation? This is still an important unsolved academic problem. Scholars have been arguing about the strategic tendency of declining enterprises. McKinley (1993) divides them into two camps: "decline is the mother of innovation" and "decline is the mother of rigidity". Scholars who advocate that decline could boost innovation cite the behavioral theory of the firm and prospect theory and claim that managers seek risks when they face performance below the average level (Cyert & March, 1963; Kahneman & Tversky, 1979). On the other hand, the scholars who advocate that decline might restrain innovation rely on the "threat-rigidity" hypothesis, and claim that decline restrain the risk-taking of management, so as to reduce the change and adaptation of the organization to avoid innovation (Staw et al., 1981). Liu Jianguo (2017), a domestic scholar, suggests in his research that performance decline increases the motivation of enterprises innovation behavior, and the larger the degree of decline, the more likely the enterprises are to achieve recovery through innovation; Tang Chaoyong and other scholars (2018; 2019) use first-hand data to verify that decline has a positive impact on organizational innovation; Li Sihai and other scholar′s research (2018) suggests that enterprises suffering performance decline have not significantly increased their R&D investment.
    The uncertainty of the relationship between enterprise decline and innovation behavior shows that the mechanism of their influence has not been fully analyzed, and there is still a need for further interpretation. The following two research hypothesis are worth thinking about: firstly, it might be to break through the dichotomy camp of "decline is the mother of innovation" and "decline is the mother of rigidity", to integrate the behavioral theory of the firm, prospect theory, and "threat-rigidity" hypothesis, and to add the point of view of survival reference point (March & Shapira,1987), it is assumed that there is a non-linear relationship between enterprise decline and innovation behavior (Chen & Miller, 2007); the second is to find the contingency factors of the relationship between enterprise decline and innovation behavior (Mone et al., 1998; Audia & Greve, 2006; Latham & Braun, 2009; Tang Chaoyong et al., 2018; 2019). Slack resources are the key to the innovation of enterprises in the state of decline. In addition, CEO is the core force of the executive team, and CEO tenure can also significantly affect the risk decision-making of enterprise innovation.
    Based on the behavioral theory of the firm, prospect theory and "threat-rigidity" hypothesis, this study analyzes the relationship between enterprise decline and innovation behavior, and discusses the regulatory effect of slack resources and CEO tenure on such relationship. By using the data of A-share manufacturing listed companies in Shanghai and Shenzhen stock markets from 2012 to 2016 and adopting the fixed effect model regression analysis, the following conclusions are obtained: (1) the relationship between enterprise decline and innovation behavior is not a simple linear one, but an inverted U-shaped one in which the intensity of enterprise innovation behavior first rises and then declines with the deepening of decline, and this finding was still valid after endogenous control and robustness test; (2) slack resources play a significant positive role in enterprise decline and innovation behavior, the more slack resources an enterprise has, the more wealth there is, it can turn to help the enterprise to innovate, to reduce the impact of decline on the enterprise, and to strengthen the ability of innovation behavior in the declining predicament; (3) the positive regulatory effect of CEO tenure on enterprise decline and innovation behavior is closely related to the degree of decline, with the deepening of the decline, its positive regulatory effect is gradually weakened. Further examination of the regulatory effect of the nature of property rights shows that the state-owned property rights play a positive regulatory role between the decline of enterprises and innovation behavior, but this regulatory role is not significant.
    The research results not only expand the previous research on the relationship between innovation and rigidity paradox of declining enterprises and the theoretical research on its scenario effect, but also provide the management with enlightenment on how to realize the reversal of the current declining enterprises in China. First of all, managers should actively face the decline. Whether the result is positive or negative depends on how the decline is managed; Secondly, enterprises are desperate to pursue innovation in the decline which may cause enterprises to fall into extreme difficulties or even bankruptcy. On the contrary, if conservative measures are taken to avoid risks, enterprises will become rigid. Therefore, enterprise managers in order to help enterprises reverse the decline and realize the recovery, they should comprehensively consider and timely take innovative actions. Finally, the implementation of innovative actions in the context of decline should be based on the evaluation of their resources and the effective use of the advantages of slack resources. At the same time, the role of CEO tenure should be concentrated to serve the innovation and development of enterprises. In addition, from the perspective of government, it is also suggested that the government′s policies should be more inclined to promote private enterprises, so as to improve the possibility of private enterprises′ strategic recovery through innovation and promote their sustainable development.