"However, you cannot will a debt. All debts must be cleared by the estate, they cannot be willed to anyone."
I think it might be no harm to add some clarification to this. Technically, it is feasible to will a debt, in the sense of making a particular beneficiary liable for it (out of the assets being received by that beneficiary - obviously no beneficiary would accept a nett liability); for example "I give my investment property at XXXXXXX to X subject to and charged with repayment of the AIB mortgage loan secured upon it"
Regarding redtigers original query. it is most unclear, but by way of general observation only:
1. When you guarantee a debt, your liability does not die with you. Your estate can be called on to honour the guarantee.
2. If the deceased was in fact making half the payments on a mortgage, there is a strong legal argument that the deceased was acquiring a beneficial interest in the property (even if this is not reflected in the title deeds).
3. Does redtiger own all of the property but want the deceased's estate to pay for half of it (by discharging half the mortgage)? This sounds like it would be highly unusual. I think it will be an uphill battle unless there is some explicit written agreement whereby the deceased in effect undertook to pay for half the mortgage(without acquiring a half interest in the property)
4. If the deceased owned a half share of the property, then it would likewise be highly unusual for a situation to emerge where the estate had a half interest in the property, but did not assume reponsiblity for half the mortgage.
these are general observations only; as other posters say, there is not enough detail to be able to give a full answer.