Translation:I thought there had been something special.
I'd concur for other verbs. But "haver" cannot do this.
Only a few specific cases can take "haver" with a subject.
Your sentence: "Eu pensei que (eu) tinha sido algo especial"
Even so, it's really not good to omit that eu. This sentence has many possible meanings with other persons, being "it" probably the first thing to come up in mind instead of "I".