The passage in question is this:
友達はかねてから国元にいる親たちに勧まない結婚を強いられていた。
Now, I recognize that kanji from 勧める, so I'm inclined to think this passage means "For some time, my friend had been pressured by his parents back home for his unadvised marriage" or something like that, but Denshi Jisho doesn't come back with any results for すすまる, and I've not encountered it elsewhere, so I'm mostly inferring this from the kanji and context.
「勧{すす}まない」＝「進{すす}まない」
This book is from a century ago: therefore, some of the kanji choices just look "different" from what one might expect by today's standards.
According to 大辞林, one of the definitions listed for 「進む」 reads:
⑧ ある事をしようという気力{きりょく}・意欲{いよく}が出てくる。積極的{せっきょくてき}になる。
= "to be willing to do something actively"
So, 「勧まない/進まない」 means the opposite of that. Thus,
「勧まない結婚」 means "a marriage that one is unwilling to go through with"
In this context I think it almost certainly means 気が進まない. 気が進まない結婚 would mean "unwanted/unwelcome marriage."
At least in modern Japanese, すすまない on its own rarely means reluctant regardless of which kanji is used. You should always use the set phrase 気が進まない.
There is also 進んで (willingly), but this is almost like a lexicalized adverb to me. We almost never say 進まないで to mean unwillingly/reluctantly.
Not the best source, but someone asked the same question on another website and was told it meant an arranged marriage that they weren't interested in/were half-hearted about.
