No, the debts are the company's. Always remember that a company is a 'person' in law. It's not the directors, it's not the shareholders, it's itself.
A big problem with buying any company is that you really don't know what the company's debts and liabilities are. You can't tell by looking at the latest accounts. Why not? Partly because accounts are a snapshot of one moment at one past time but mainly because the company may have contracts and any number of other obligations, all of which are or may translate into debts due now or tomorrow, or next year, whenever,but they are all out there. These liabilities won't show on the accounts, and may not be readily detectable either.
If you think that problematic, you are not alone. There have been recent instances of major public companies taking over other big companies, only to discover , too late, that the bought business had vastly greater debts and liabilities (and sometimes far less in assets) than they knew of