Since I saw your question, I have held back so as not to cause your post to disappear off the unanswered list before someone very knowledgeable replies. Below are my thoughts but I am not an expert.
Sharing the debt would not provide your daughter with any added protection against eviction from her present home whereas sharing ownership almost certainly would - these two things are separate. Ownership, in a way, has nothing to do with a mortgage although usually only the owner would get a mortgage (partial or whole responsibility for repayment). Simply owing money on a property does not confer ownership, in fact the opposite because directly proportional to the outstanding amount (and through the signed security for the loan) ownership in a sense rests with the lender until the debt is paid. If a share of the ownership were transferred to your daughter then the mortgage issuer would have to be advised (the process more or less guarantees this) and that institution (bank or building society) might not agree and/or would attach conditions for the loan to continue, possibly including a completely new loan and terms.
If your daughter takes on a share of the mortgage without securing ownership to at least the proportional extent then she has the worst of everything: She would owe money on the property, not own any part of it and have no defence against the owner or his creditors (to whom he is in debt) if they (either/any of them) tell her to vacate it.
Any action resulting from debt owed by her (former) partner could impinge on your daughter where hers and his financial affairs overlap but if she owns a share of the property then, as a separate individual, she would retain that ownership regardless of the other owner losing his. If hers is a minority ownership then issues pertaining to the majority ownership could easily overrule her security of tenure, but not her partial ownership in itself. A sale of the property could then possibly be forced but your daughter should get her share of the net proceeds. As a minority owner in this scenario she would most likely have to vacate the property, possibly even as a majority owner but not as sole owner. The issue would likely be regarded as complicated and all procedures could be very long winded. None of this would however apply if she simply shared the debt (mortgage) because then she could be evicted with the minimum statutory notice and have no say at all if/when he is forced to sell by a creditor such as the taxman.
You are correct to fear the possibility that the taxman could ultimately seize the property in order to sell it against a debt owed them b y the owner (partial or sole), although this might take some time to bring about. The tax authorities are the most powerful authority in the land.
Hopefully someone properly knowledgeable will provide you with a more authoritative and comprehensive response.