I’m a bit confused. I thought that monks are cloistered (just as nuns are), and so one wouldn’t see a monk or nun at Daily Mass. Are you sure you didn’t see a religious brother?
Monks are not behind a strict enclosure, they’re behind a simple enclosure. Nuns however maintain the strict enclosure, except for one or two “externals” who are responsible for running errands, etc.
That said, even cloistered monks do get out and about. For one, monasteries always have an endless list of errands in town that need to be run. Secondly, monks often go to conferences either as speakers or audience; they go to classes outside of the monastery. They can also be given permission to leave the enclosure for special family events (parent’s 50th anniversary, be at the bedside of a dying parent, funerals, baptisms, etc.). In our abbey the Oblate Master travels do Montreal and Quebec City for two annual oblate’s meetings. The choirmaster and abbot (an accomplished organist) often teach courses, give seminars, etc. on the organ and Gregorian chant. I ran into our choirmaster at a daily Mass in Montreal a couple of years ago, at St. Joseph’s oratory, he was there to attend a music conference. They also travel to other monasteries to lend a hand where needed, learn a craft, etc., and will of course leave the monastery from time to time for medical/dental appointments.
In short, they don’t
habitually leave the enclosure, but they do on occasion leave the enclosure, and when they do, they will attend the liturgies of the places they are visiting. They never however, leave the enclosure without permission from the superior, and never without first receiving his blessing, even if going out for weekly errands.
Nuns are behind a strict enclosure (sometimes called “strict papal enclosure”) and are a different story altogether. The non-cloistered “external” nuns handle the errands, and the cloistered nuns typically won’t go out except for very grave reasons.