There are two acceptable excuses for not-fasting which are being sick and traveling. These people have to fast some other days after Ramadan in order to fulfill their duties. They do not have any other duty besides that. The Almighty God decrees:
“(The prescribed fast is for) a certain number of days. Whoever among you does not fast on those days because you are sick or on a journey, then (you should fast) the same number of days on other days. Those who are able to fast are also required to pay a fee (which is equivalent to the cost) of feeding a desperate person. Whoever volunteers to do more than good (which is paying more than bound to be paid), it is better for them. If only you knew how good it is for you to fast, you would (in spite of being sick or on journey). Ramadan is the month when the Quran had been sent down, that Criterion which is a guide for people and which also includes the explanatory verses of that guide. So, whoever among you witnesses that month must spend it by fasting. Whoever is sick or on a journey may fast for the same number of days on other days. God desires ease for you. He does not desire difficulty. These eases are in order that you complete the number of days and (at the end of fasting) you glorify God (during the prayer of Eid) for guiding you to this, and that you fulfill your duties towards Him.” (Al-Baqarah 2:184-185)
People who did not fast for other reasons cannot do anything to compensate for what they did. The only choice they have in order to be forgiven is to repent and never do it again.