She did not observe ‘iddah following her husband’s death because she thought that ‘iddah was only required for a woman whose marriage had been consummated

Firstly: 

There is a difference between ‘iddah following the husband’s
death and ‘iddah following divorce. With regard to ‘iddah following the
husband’s death, there is no stipulation that the marriage should have been
consummated. Any woman whose husband dies, even before consummation of the
marriage, is obliged to observe ‘iddah, because of the general meaning of
the verse in which Allah, may He be exalted, says (interpretation of the
meaning):

“And those of
you who die and leave wives behind them, they (the wives) shall wait (as
regards their marriage) for four months and ten days”

[al-Baqarah 2:234]. 

At-Tirmidhi (may Allah have mercy on him) narrated from Ibn
Mas‘ood (may Allah be pleased with him) that he was asked about a man who
married a woman and did not state her dowry or consummate the marriage with
her before he died. Ibn Mas‘ood (may Allah be pleased with him) said: She
should be given a dowry like that of women who are similar to her, no more
and no less, and she has to observe the ‘iddah, and she is entitled to the
inheritance. Ma‘qool ibn Sinaan al-Ashja‘i (may Allah be pleased with him)
stood up and said: The Messenger of Allah (blessings and peace of Allah be
upon him) issued a ruling concerning Birwa‘ bint Waashiq, one of our
womenfolk, that was like the ruling you have given. Ibn Mas‘ood was happy
with this (news).

Classed as saheeh by Shaykh al-Albaani (may Allah have mercy
on him) in Saheeh Sunan at-Tirmidhi. 

With regard to ‘iddah following divorce, it is obligatory for
the woman with whom the marriage was consummated; as for the one with whom
it was not consummated, she is not obliged to observe ‘iddah, because Allah,
may He be exalted, says (interpretation of the meaning):

“O you who
believe! When you marry believing women, and then divorce them before you
have sexual intercourse with them, no ‘Iddah (divorce prescribed period)
have you to count in respect of them”

[al-Ahzaab 33:49]. 

Abu Bakr ibn al-‘Arabi (may Allah have mercy on him) said:
This verse states that no ‘iddah is required of a woman who is divorced
before the marriage is consummated. This is the consensus of the ummah,
because of this verse. But if he has consummated the marriage with her, then
she must observe ‘iddah, according to scholarly consensus.

End quote from Ahkaam al-Qur’an (6/377) 

For more information, please see the answer to question no.
120018 

Secondly: 

If a woman fails to observe ‘iddah following her husband’s
death out of ignorance, she does not have to do anything if the time for the
‘iddah has ended. But if there is still any of the ‘iddah period remaining,
she must observe ‘iddah for the remainder of that period. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked
about a woman who did not observe ‘iddah following her husband’s death,
because she was unaware of this obligation; what is the ruling on that? 

He replied: She does not have to do anything so long as she
omitted to observe the mourning period out of ignorance, because Allah, may
He be exalted, says (interpretation of the meaning):

“And there is
no sin on you if you make a mistake therein, except in regard to what your
hearts deliberately intend”

[Al-Ahzaab 33:5]

“Our Lord!
Punish us not if we forget or fall into error”

[al-Baqarah 2:286].

And Allah, may He be exalted, said: I have done that. 

[The questioner] asked: O shaykh, what if she has come to
know of the ruling now? 

He (may Allah have mercy on him) replied: If she found out
after the end of the ‘iddah, she does not have to do anything, but if she
found out during it, then she should observe ‘iddah for thr remainder of
that period.

End quote from Fataawa Noor ‘ala ad-Darb. 

Based on that, that woman does not have to do anything with
regard to what has passed, because she was unaware of the ruling, but with
regard to the remainder of the ‘iddah period, which is two months and ten
days, she must observe ‘iddah during that time. 

And Allah knows best.