What does のが in 私は一人でいるのが好きです。mean exactly?
( Translation: I like being alone.)
I think it is better to think of 「の」 and 「が」 as separate particles.
「の」 here is used to make the verb 「いる」 into a name (kind of like an infinitive, maybe?) “to be alone”, or “being alone”.
「が」 is then used in the usual way as the subject marker for 「好き」.
Here is a pretty extensive explanation (also for 「こと」):
https://www.wasabi-jpn.com/japanese-grammar/nominalizers-koto-and-no/
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