She did not fast because she was pregnant and breast-feeding, and she did not make up the missed fasts until she got old and became unable to make them up, then she died. Can fasts be done on her behalf?

Firstly:

If a woman does not fast because of pregnancy and breast-feeding, then she should make up the fast only, whether she broke the fast out of fear for herself or out of fear for her foetus, according to the correct view, as has been explained previously in the answer to question no. 49794.

Secondly:

If your aunt had delayed making up the fasts for a valid reason, then she became unable to make them up because she had grown old and was unable to do so, then for each day she should have fed one poor person half a saa‘ of rice or other (staple food).

Now her heirs should pay from her estate to feed the poor in this manner. If she was able to make up the fasts before she grew old, but did not do that until the next Ramadan came, then she became unable to make up the fasts, then she must feed one poor person for each day, and offer expiation for delaying making up the fasts with no excuse; that is the view of the majority of fuqaha’.

The expiation is to feed one poor person for each day; the expiation is not multiplied by the number of years [that passed without making up the fast].

See the answer to question no. 26865.

Based on that, she should have fed two poor persons for each day: one instead of fasting, and the other is expiation for delaying making up the fasts without any excuse.

If she did not do that before she died, then that should be paid for out of her estate.

That is to be on the safe side.

Some of the scholars are of the view that there is no expiation for delaying making up missed fasts; what is required in their view is to feed one poor person for each day. See the answer to question no. 26865.

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked about a woman who did not make up the days of her menses in Ramadan, until she accumulated approximately two hundred days. Now she is sick and elderly, and cannot fast. What should she do?

He replied: if this woman is as the questioner described, and will be harmed by fasting because she is old and sick, then one poor person should be fed for every day on her behalf, so she should work out the number of days missed, and feed one poor person for each day.

End quote from Fataawa as-Siyaam (p. 121).

Thus it is known that there is no fasting to be made up on her behalf, so there is no need  for her heir or anyone else to fast on her behalf.

And Allah knows best.