It will never become an "adjective" whatever you do with it. But you can make it be a clause that acts as a qualifier. Just as 日本語の分からない qualifies 人.
If you use a verb:
この人が食べたケーキ。 : The cake that this person ate
If you use an adjective:
優しいこの人。 : This person, who is nice
Other examples:
目の前に現れた人。 : The person that appeared in front of my eyes
机の上にいる猫。 : The cat that is on the desk
The noun that comes after the verb/adjective is qualified by the previous relative clause.