She stopped praying when she was sick, then she died; do her heirs have to do anything?

Firstly: 

Prayer is one of the greatest pillars of
Islam after the Shahaadatayn (twin declaration of faith). What the Muslim
must do is always offer the prayers regularly and on time; this duty is not
waived so long as he is of sound mind. 

For more information, please see the answer
to question no. 95220. 

Secondly: 

You did not say whether your mother had
become unconscious and thus was not aware of anything, or not. However it
appears from your question that she was of sound mind at the time of her
illness, based on the fact that she intended to make up those prayers. In
general, the one who does not pray in the case of illness must come under
one of the following two scenarios:

1.    
He stopped praying when he was sick because he had lost his mind or
lost consciousness. In this case he does not have to do anything, in sha
Allah, and he is not obliged to make up the prayers when he recovers after
that.

2.    
He stopped praying when he was sick but was still of sound mind; but
he stopped praying because he thought that prayer was not obligatory for him
in that situation. In this case, perhaps Allah will pardon him because of
his ignorance, although what the individual is required to do is to learn
what he must know of his religion.

In either case, the prayers are not to be
made up on his behalf if he dies after that. 

It says in Fataawa al-Lajnah ad-Daa’imah
(25/257):

If your father was unconscious at the time
of his illness and did not understand anything, then the obligation of
prayer was waived in his case, and he is not accountable when he is in this
state. The condition of being accountable for prayer is that the individual
should be of sound mind (and not unconscious), and that was not the case
here. But if he was not unconscious and was of sound mind, but he did not
pray because he was unaware that it is obligatory for people in his
situation to pray according to what they are able to do, then perhaps Allah
will pardon him and excuse him because he was unaware of that, and because
there was no one who could explain the shar‘i ruling to him before he died –
may Allah have mercy on him and forgive him. In either case, it is not
permissible for you to offer any of the prayers on your father’s behalf,
because one cannot pray on behalf of anyone else. The basic ruling is that
prayer cannot be delegated to another person. End quote. 

Thirdly: 

With regard to making up the fasts, if she
did not make them up with no excuse, then it is mustahabb for you to fast on
her behalf, because of the report narrated by al-Bukhaari (1952) and Muslim
(1935) from the hadeeth of ‘Aa’ishah (may Allah be pleased with her),
according to which the Prophet (blessings and peace of Allah be upon him)
said: “If anyone dies still owing fasts, let his heir fast on his behalf.” 

For more information, please see the answers
to questions no. 130283 and
130647 

It is permissible for making up of the fasts
on behalf of the deceased to be done by one heir for all of the days, or it
may be done by a number of heirs. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy
on him) said:

Question: If we follow the more correct
opinion, which is that fasting includes that which is obligatory because of
basic Islamic teachings and that which is obligatory because of a vow
(nadhr), does that mean that this (making up the fasts of behalf of the
deceased) is to be done by one of the heirs only, because fasting was
obligatory upon one person only?

Answer: It does not mean that, because the
words of the Prophet (blessings and peace of Allah be upon him), “let his
heir fast on his behalf” include all the heirs. So if we assume that a man
has fifteen sons, and each of them wants to fast two out of thirty days,
that is acceptable. If there are thirty heirs and each of them fasts one
day, that is acceptable, because they will have fasted thirty days. It makes
no difference whether they fast on one day, or one fasts on one day, then
the second one fasts on the next day, (and so on) until they have completed
thirty days.

End quote from ash-Sharh al-Mumti‘
(6/452) 

Fourthly: 

If a person performs Hajj or ‘Umrah on
behalf of his parents, and he has performed Hajj on his own behalf before
that, then the reward of that Hajj or ‘Umrah will reach his parents, and
that action on the part of the son will be a kind of honouring and kindness
towards his parents. 

Muslim (1939) narrated from ‘Abdullah ibn
Buraydah that his father (may Allah be pleased with him) said: Whilst I was
sitting with the Messenger of Allah (blessings and peace of Allah be upon
him), a woman came to him and said: I gave a slave woman in charity to my
mother, who has now died. He said: “Your reward is due; you may take (the
slave woman) back by virtue of your inheritance.” She said: O Messenger of
Allah, she owes one month’s fast; can I fast on her behalf? He said: “Fast
on her behalf.” She said: She never did Hajj; can I do Hajj on her behalf?
He said: “Do Hajj on her behalf.” 

It says in Fataawa al-Lajnah ad-Daa’imah
(25/257): With regard to your doing Hajj and ‘umrah on behalf of your
father, that is part of honouring him and showing kindness to him. And if
you give charity on his behalf from time to time, and you offer supplication
for him, pray for forgiveness for him, uphold ties of kinship with his
relatives, and treat his friends kindly, then that is a way of honouring
your father after his death, and you will have a great reward, in sha Allah,
for whatever you spend for that purpose. End quote. 

For more information, please see the answers
to questions no. 763 and 104606 

And Allah knows best.