If a priest is a diocesan priest, he is a secular man. Therefore, he must have a retirement plan. Most dioceses provide a retirement plan similar to a 401K or an actual 401K. Because diocesan priests are secular men, they also pay taxes. This includes FICA. They have social security benefits. They get paid a salary for their work. It is not a large amount compared to other professionals with the same level of education and similar level of responsibilities. But most diocesan priests retire on these plans and any money that they may have from other sources such as family funds. Since they are secular, they can retire anywhere they want. They can purchase a home of their own, live with their family, get an apartment in an assisted living setting or with friends. Some dioceses allow older priests to live in one of their rectories, if there is room. The priest pays rent to live there or he provides some services to the parish, such as helping with mass on Sundays and weekly confessions. This helps the parish and keeps the priest connected to ministry.
If a priest is a consecrated religious he does not retire. Religious never retire, per se. He will always be a religious: Dominican, Franciscan, Jesuit, etc. Religious continue to live with their religoius community until they die. If they have poor health and need special care the religious community provides that care. Some communities have a mother house where the central government of the region is located. These houses are usually large enough to provide housing for those religious who need special care and there are usually other religious men who provide the care or the community pays nurses to come in to do so. Also, many religious communities of men assign their older men to their houses of formation. These men are a wonderful inspiration to the younger men in training. This way they have a home, a family and continue to participate in community life.
When I was a novice we had two friars living in our novitiate who were too old and fragile to be out in a regular community house with too much activity. The novitiate was wonderful for them because the novices took care of all their needs and they were a splendid example of Franciscan life for us. They even taught a few classes to the novices.
Priests who are consecrated religious have to be cared for by their community. It is the obligation of the community to do so. In addition, religious do not have retirement plans or social security, because the vow of poverty does ot allow for this. Some religious communities have medical insurance and that’s it. Many do not have that either.
I hope this helps.
Br. JR, OSF