Why do the Middle English words, that stay after "to" haven't got the Middle English infinitive ending "n"?
Wycliffe's Bible
Luke.16:3
"And the baili seide with ynne him silf, What schal Y do, for my lord takith awei fro me the baili? delfe mai Y not, I schame to begge."
King James Bible:
"Then the steward said within himself, What shall I do? for my lord taketh away from me the stewardship: I cannot dig; to beg I am ashamed."
I have been studying the 'Wycliffe Manuscript New Testament' facsimile published by James A. Fowler of CIY. Wycliffe produced his translation in the late 1300s, and the manuscript of which I have this facsimile is thought to have been written in around about 1400. In this scribe's English, infinitives mostly seem to be the root plus -e. E.g. "many seeken TO ENTRE and thei schulen not mowe" (many seek TO ENTER and they shall not be able). The root is ENTR-. Infinitive = ENTRE. I am puzzled that Wiktionary (to which you give a link) says Middle English infinitive of to beg was beggen. I suspect that is a mistake, or an earlier time in Middle English, or a different region. I do not think I have seen any infinitive ending -en so far in this Wycliffe New Testament.
Why do the Middle English words, that stay after "to" haven't got the Middle English infinitive ending "n"?
I suspect that this is too much of a generalisation: some do, some don't.
The OED offers the following examples. You will note that there is not a lot of regularity. This is not surprising as it was not until the 18th century that spelling began to be standardised.
In Old and Middle English, many words were written as the writer heard them or in a “house-style”.
NB the quote of 1377, which is contemporaneous with Wycliffe.
1. To ask alms or by way of alms.
a. transitive. To ask (bread, money, etc.) in alms or as a charitable gift; to procure (one's living) by begging.
?c1225 (▸?a1200) Ancrene Riwle (Cleo. C.vi) (1972) 263 Scheome ich cleopie eauer her..beggen as an harlot..his liuenað.
1377 W. Langland Piers Plowman B. vi. 195 Blynde and bedreden..þat seten to begge silver.
c1440 Promptorium Parvulorum 28/2 Beggyn bodely fode.
c1500 Bk. Mayd Emlyn xxvii, in Poet. Tracts (Percy Soc.) 28 Longe or she were dede, She wente to begge her brede.
b. intransitive. To ask alms; esp. to ask alms habitually, to live by asking alms. Const. absol.; of, from, formerly at, a person; for alms.
1386 G. Chaucer Summoner's Tale 4 Ther wente a lymytour aboute To preche and eek to begge.
a1450 York Myst., Barbers 8 What riche man gose from dore to dore To begge at hym þat has right noght.
Further complications wwere
He went to help his friends = He went to the help(dative) of his friends(genitive).
