If the business is a limited company then it is the company that has the debt, not the shareholders. The "limited" in "limited company" essentially means that, once shareholders have paid the company for their shares, they have no further debt to the company or to its creditors.
At least, that's what I gather from a perusal of the literature. I hope that's right, since I do have shares in a limited company that has a high debt to equity ratio.
My advice to you would be to get legal advice from a professional
Personally, If you don't legally sign for that business, I dont think you could be held 100% responsible for the debts.... however, if NO ONE takes over the business when your father in law passes away then it would probably depend on which banks he has taken out the personal loans / credit cards and what insurance he has on these loans...
Any money / assest he happens to have will be frozen so the creditors get paid first ie: house, boat, car etc... if no one takes over the business, these banks will want their money and they will be entitled to any assets first before anything can be inherited.