Lisapower, as Vinny has detailed, there is a path from a time-limited spouse visa to ILR, notwithstanding the death of the sponsor, as long as the marriage was subsisting up to the time of the death.
However, what there is not .... in the immigration rules .... is a path from a fiancé(e) visa to ILR. That is, let's assume the person comes to the UK on a fiancé(e) visa, and either the marriage has not yet happened, or it has happened, but the person has not yet got round to converting that visa into a spouse visa, using form FLR(M). In these circumstances there is nothing in the rules to permit conversion into ILR.
Hint .... after the marriage has happened ... convert into a spouse visa without delay!