Can I be forced to honour supplier contracts the failing business signed right before it collapsed?

Generally, no. In an asset purchase, a buyer only takes on the contracts it expressly agrees to assume in the purchase agreement, so supplier contracts the seller signed are not automatically binding on you just because you bought some of the seller's assets. This holds true even for contracts signed shortly before the business collapsed, unless you specifically agree to step into them.

The exception is where you actually want, or need, a particular supplier contract to keep operating and negotiate to have it assigned or assumed as part of the deal, which typically also requires the supplier's consent, since a contract usually can't be transferred to a new party without the other side agreeing. During due diligence, get a full list of the seller's material contracts and go through them one by one, making clear which ones are, and are not, coming along with the purchase, rather than leaving the question open and assuming the answer is obvious.