Understand the cause and indirect infulence - Call your FIL, say I heard from my wife that business is not going well, what happened etc and get to know the whole story.
If he has lenders dancing on his head, then it means he overspent on the business than it can generate and now you are just going to repay the lenders/banks whatever. You will not get anything back as he was not able to make that money before from his business. Sunk Cost.
If he has some intermittent finance problems, like vendor payments etc and he has good revenue, then it could make sense to infuse some capital in tranches to make him clear the payments and get things running, make it back again.
If he has alternative financing on the way, well and good, you can stop worrying. If no, then you can say oh no, then how are you going to do it? Are you going to mortgage your house/ Selling gold? Are you going to close the shop? - Indirectly conveying and saying to own up the responsibility.
Past history - If your FIL has a bad history of making poor financial decisions or great financial decisions. It helps too.
Repayment capacity and you net worth - If you wanna lend, consider how much he can repay each month, ideally if you cant recover in 2 years time, then you are just donating. If you are cash rich, like, 2-4cr in cash, then I guess you can consider helping, but if you are close to 1cr then, No.
Wife - Your wife staying silent doesn't mean she wants you to help at any cost. She may also be thinking how to say No to papa, maybe he will say No and I can use his name and not make papa feel bad. It is common to think this way. Speak to your wife and act like its a very big amount, I dont think we can afford it etc etc and slowly convince her. Women understand reasoning better than straight forward No or okay.