When a relative pronoun

has a subject gap, it is optional. The parent can be altered to correct or to add etc.

Every that -relative clause has a gap, a missing constituent that’s linked to the modified noun phrase. I want a house i _(subject gap) Note _that the subject in the relative clause

is missing, but it’s anaphorically linked to the noun “house”. When the gap is in the subject position, the relative pronoun is obligatory, at least in standard English; hence, the ungrammatical sentence below.

I live in the house I (object gap) Since the _missing constituent in the relative clause _is the direct object of

the verb “sold”, the omission of the relative pronoun wont make the sentence ungrammatical.