I don't think it's just a matter of modals allowing a (pseudo)passive construction. I don't know of any theoretical reason why modals would be expected to have such an effect, and I would not classify 31c) or 32c) as acceptable sentences.
(It's harder for me to say whether they are "possible", because they are "possible" in a certain sense: e.g. I might come up with 31c) if I was forced to provide a passive version of "His father can walk around Seoul". But I think I likewise might produce 31a) if I was forced to provide a passive version of "His father walked around Seoul.")
32b) actually doesn't sound very acceptable to me to begin with, but "The hotel was stayed in by foreigners" doesn't sound much worse, whereas your 32c) "The hotel can be stayed in by my sister" definitely sounds more unnatural/unacceptable to me than either.
Likewise, "walked around" sounds as acceptable to me in the following sentences (taken from the web) as it does in 31b) (that is, it sounds like fairly awkward wording in all of these sentences):
By faith, the walls of Jericho fell, after it was walked around for seven days.
–"Aramaic Bible in Plain English" (a translation, of course, but the translator presumably wasn't aiming to produce an outright unacceptable or ungrammatical sentence.)
This lake was treated in 1954 and planted with rainbow trout in 1955.
The lake was walked around completely and no fish were observed from shore, although a number were seen jumping for flies. One 6" rainbow trout was found dead (winter kill?). It appeared to be in good condition.
–the first of three paragraphs in the one-page "File Note: Woods Lake, Alpine County." July 25, 1956. From California Department of Fish and Wildlife’s (CDFW) Data Portal.
Your 31c) "Seoul can be walked around by his father" doesn't sound much, if at all, better to me than 31a) "Seoul was walked around by his father." I'd say both sound less acceptable than the examples above with "walked around".