While more can always be said, I hope my previous post in: Was it common for pre-modern Catholic monks and nuns to join monasteries/nunneries without religious callings because they didn't want to starve? To what degree were these places "employers," of last resort? Were unenthusiastic members a drag on their communities? might offer some basic guidelines to consider OP's question.

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In short, the overall prospective wouldn't look so promising, and would also depend on which area within Europe the beggar lived in.

Based on what I illustrated in the linked thread, the most promising receiving sides of OP's beggar in Medieval Europe would be:

• Lay Brothers (conversi) of the Cistercians (12th and 13th centuries)
• (a kind of official lay supporter, not full members......) The Third Order of Saint Francis for the Franciscans (13th centuries and later)
• (The most promising, but......) semi-monastic Beguines and Beghards (mainly 13th century and later)

These "orders" had some individual difficulties for OP's beggar to be accepted, however.

First of all, as I also illustrated in the linked post, the "disparity" between the full brother and lay brother in the Cistercians sometimes led to the disobedience of the latter group, comprising also of non-noble origin, so It might be a difficult for religiously motivated OP's beggar could put up with the circumstances within the cloister. It might also be not so easy for the beggar (I assume they could mainly live in medieval cities rather than in the countryside) to find the Cistercian monastery in cities.

The Franciscans also certainly provided the convenient option for the religiously aspirant lay people in form of their Third Order, and they would be much easier to find and to get familiar with in different cities in later medieval Europe. The biggest drawback for the Third Order was, however, that they were not full member of the order with the monastic vow - and this system perhaps also make it harder for OP's beggar to be admitted into the order with the official monastic vow.

On the other hand, Beguines (females) and Beghards (males) found mainly in the Low Countries would be much more realistic options for non-noble lay aspirants, since they were basically "amateur" semi-monastic sisterhood and brotherhood who often lived in communal life with some religious activities like praying and reading the book, though without strict and official monastic vow. Initial members of the Humiliati in northern Italy had also been kind of similar half-lay half-religious fraternities, but after its official approval by Pope Innocent III, this "order" was unfortunately also streamlined into the subdivision including the lay "third order" system.

The following were main drawbacks for the Beguines/ Beghards, though:

• They were found almost only in urbanized areas within medieval Europe like the Low Countries, so, the availability of living as a one of them could not be guaranteed everywhere in medieval Europe.
• I suppose that even they didn't primarily come from the lowest social stratum of medieval town, but rather drawn mainly from the middle class or better.
• Their status were not defined primarily by the monastic vow, and sometimes made vulnerable by criticisms of both the central and the local church authority - such as the ban against them promulgated by the Council of Vienne in 1312 (but the majority of them seemed to keep at least survived after this ban). They could sometimes (though not so often) be victims of the inquisition (especially if the beggar in question said something about the vision from the God as mentioned in OP).

As for female Beguines, this recent post by /u/jellolegos in: Could a married woman become a nun without her husband's approval in 1100-1500s Western Europe? For instance, to run-away from domestic violence might also be much more useful than mine.

Recommended Related Literature:

• Miller, Tanya Stabler. The Beguines of Medieval Paris: Gender, Patronage, and Spiritual Authority. Philadelphia, PA: U of Penn P, 2014.
• Simons, Walter. Cities of Ladies: Beguine Communities in the Medieval Low Countries, 1200-1565. Philadelphia, PA: U of Penn P, 2001.

(Edited): fixes typo.