"I know what I like"
That's some really good questions. I'd be interesting to know this as well.
I'm raking my brain, but I can't seem to come up with an example where what is used as a relative pronoun.
In the above sentence I don't think "what" introduces a subordinate clause.
It's weird, Englishplus.com doesn't seem to consider "what" as relative pronoun:
"Relative Pronoun A relative pronoun "relates" a subordinate clause to the rest of the sentence. It may be found in adjective and noun clauses.
A relative pronoun is found only in sentences with more than one clause.
In modern English there are five relative pronouns: that, which, who, whom, and whose.
All but that can also be interrogative pronouns. That may also be a demonstrative pronoun.
In addition, these pronouns may take the suffixes -ever and -soever."
I checked the glossary on this website and came up with a similar answer:
"Relative pronouns, such as That, Who, Which, Whose and Whom can be used to introduce clauses in sentences"
None of them refer to "what" as a relative pronoun. I know in your example it's not an interrogative pronoun but I don't know what kind of pronoun it is.