In addition to the above answer I can offer you one unique example of a young woman giving up her religious vows.

Christina Carpenter became an anchoress in the small village of Shere in Surrey, England in the first half of the 14th century. An anchorite (male) or anchoress (female) is a person who takes a vow of stability and is attached to a church in a cell with no exit, literally built into the wall of the church where they would live until death. It was a fairly extreme expression of devotion but one that came with certain amounts of prestige and power, particularly for women who may not have the same opportunities to gain religious authority as men. People would travel to seek wisdom from an anchoress and they could become pilgrimage sites in their own right. A famous example of an anchoress is Julian of Norwich the author of Revelations of Divine Love.

Anyway, Christina Carpenter is interesting because her cell was built on to the outer wall of St James's church in Shere, where she just had a portal to receive food, speak to visitors and receive the body and blood of Christ during mass, but, after an unspecified amount of time she wanted to leave. And so, she left. The wall was broken down and she returned to live the life of a lay person.

However, the reason we know this is because we have a letter written declaring that she wished to be readmitted into the cell. The bishop who was the recipient of the letter agreed that she could be readmitted to the cell if she completed some penance, as long as this time, she remained in the cell indefinitely. Records suggest the second cell had smaller holes and a squint that could be used to see the altar during services.

We don't know what happened to Christina after this, but we do know that she took an extreme religious vow, changed her mind, and then, changed her mind again back in favour of the vow. One has to wonder, if it was possible, though punished with penance, to break a vow where you have declared yourself "dead to the material world", it may have been possible to do the same in other monastic contexts.

Nine hundred ninety-five.

That's how many cases related to people leaving or switching religious communities that we know were reported to the pope from just two dioceses in 15th century Germany (Augsburg and Constance).

That includes monks, nuns, and other religious asking permission to leave; ones who left asking permission to return; and cases involving people who left and were caught.

The supplication letters also cover cases of people who were caught out on a temporary lark (running off to a tavern or brothel for a night), left for longer, or wished to switch from one community to another, which was a violation of monastic rules as well ("stability" was another vow). It includes people asking permission to leave, and superiors asking permission to kick them out. It's necessary to include all of those cases because one type of situation could easily be spun into another in hopes or more lenient or harsher treatment.

So yes: contrary to some earlier answers in this thread, it was both possible and done to break monastic vows in the Middle Ages.

It must be said first, though, that your proposed scenario of leaving to take care of your parents is unlikely. If you're concerned about their aging and their ailing health, the best thing you can do for them is...stay in your convent! Religious houses were the best and swankiest retirement communities and nursing homes in the western Middle Ages. Plus, people hoped it would provide them an advantage in the afterlife admissions and placement competition. And one major reason for a family to support the entrance of a child into religious life (i.e. pay the monastery) was to maintain a relationship with that house--it was by no means a guaranteed thing.

(Quick terminology note: when I use "religious [x]" here, it refers to monks, nuns, and others who took religious vows--religio for most of the Middle Ages referred to "rule"/way of life, in the sense of following a monastic Rule. I'm also using monastery and convent interchangeably--the difference is NOT gender, it's what order people belonged to, so just read either word as inclusive.)

In the papal letters and other topical sources, like example stories to warn readers away from leaving religious life, there are a variety of oft-repeated reasons for leaving cloister. Some were quite licit (and could thus be used as an excuse for people with other motives): permission to go on a specific pilgrimage; wanting to move to a house with stricter rule enforcement. Another set of licit reasons was pragmatic: conflict within the community; needing to flee a specific location for safety during wartime.

There were also the cases that could become licit, for example, a family wishing their daughter or prospective daughter-in-law to enter an advantageous marriage. Enough money and political clout could find some irregularity or other in the original vows. (It seems likely that many of these cases, though not all, would be involuntary departures.)

And then there were the salacious details that anticlerical late medieval and Reformation polemic just loved, about monks keeping secret families and nuns being hypocrites and so forth. Did this happen? Sure, sometimes. Alexander Murray talks about one eleventh or twelfth century (I think twelfth) abbot who, when forced to cut himself off from his extracloister "wife" and children, committed suicide. Was it as common as early Protestant polemicists liked to say? That...would not be possible, haha.

How to make your escape? As the papal supplication letters indicate, there was always the tried-and-true, but not guaranteed, method of asking for permission and receiving it. You could also go on pilgrimage and just...never come back. Some monks were assigned to go to university to study law or some such, to help their house in the future--living in the world or in the cloister afterwards. (Yes, university students included monks who were technically vowed to spend their entire lives in one place.) This, of course, was not an option for women.

But most importantly, monastic cloisters were not prisons (except when they were used as such for individual criminals--Joan of Arc's original sentence was perpetual confinement in a convent). Even for women, the strictest claustration is associated with the early modern era and maybe some 15th century Observant (i.e. monastic rules levelled up) houses. Members went on errands to procure food, beg for alms (i.e. collect donations), and so forth. There were plenty of chances to, like pilgrimage, just forget to return.

Hence the ambiguity in recorded cases between "left temporarily" and "left/tried to leave for good." Very easy to spin either one of those into the other.

As for consequences for leaving, whether or not you were caught? The primary problem with life after fleeing a cloister was the high potential for poverty. Monks (who, by the later Middle Ages, were all priests) could not work as priests-for-hire, since they were forbidden to officiate sacraments and perform other religious duties (and would have no one to vouch that they were ordained). Cities did have substantial populations of never-married women, not to mention widows, but they were overwhelmingly lower class--servants, laundresses, manual laborers.

Getting caught brought its own world of problems, and I'm not talking about corporal punishment--that was par for the course for infractions in day-to-day life, especially in monasteries. (Laugh too often? Whisper a snarky comment during communal prayers?) So were punishments like extra fasting days or labor duties for a time. For larger infractions, you could look forward to more severe fasting limitations, harsher duties, separation from other community members, loss of any kind of rank within the community, and so on.

And that's assuming they let you back in at all, instead of forcing you to stay excommunicated. In other words: hellbound.