Legal Question in Insurance Law in Illinois

There could be, yes.

If there is a trust, there has to be a trustee. if it is a "land trust" with a company like Chicago Title or something as the trustee, that kind of trustee does NOT buy insurance, the beneficiaries do. If it is a "living trust" or one set up through a will (a "testamentary trust") then the trustee is supposed to buy the insurance, and it should be in the name of the trust or trustee. The problem is that if there is a claim the insurance company may NOT owe a duty to defend to anyone other than the named insured, who is dead... But this is not the bigger issue since a call to the agent could fix this.

The HELOC could be a time bomb. You need to have someone look at the paperwork. If it was taken out in the name of the trust or the trustee, still there may be some clause in it that could let the lender call the loan because of the death. There is just no way to tell without looking at the loan documents.