Is there a sentence fragment?
On November 3, 1957, the Soviet Union sent the first animal into space—a dog named Laika. Which had been found as a stray living on the streets of Moscow.
no yes
A sentence is a group of words that expresses a complete thought.
The band I'm in has been rehearsing daily because we have a concert in two weeks.
A sentence fragment is a group of words that does not express a complete thought.
Rehearsing daily because we have a concert in two weeks.
This fragment is missing a subject. It doesn't tell who is rehearsing.
The band I'm in.
This fragment is missing a verb. It doesn't tell what the band I'm in is doing.
Because we have a concert in two weeks.
This fragment is missing an independent clause. It doesn't tell what happened because of the concert.
There is a sentence fragment that does not express a complete thought.
On November 3, 1957, the Soviet Union sent the first animal into space—a dog named Laika. Which had been found as a stray living on the streets of Moscow.
Here is one way to fix the sentence fragment:
On November 3, 1957, the Soviet Union sent the first animal into space—a dog named Laika, which had been found as a stray living on the streets of Moscow.