「あっ いや 盗ってませんから」 とはどういう意味ですか?

質問を翻訳

@lilah0236 As you say, I think the から is derived from the one meaning “because”. For example, a mother asks her daughter who left a table with her meal behind if she won’t eat a meal any more like;
A: Hey honey. You won’t eat it any more?
B: Just leave it there. 食べるから

食べるから here means “because I’ll eat.” So the full sentence will be “Just leave it there because I’ll eat.” In this way, I think a sentence ending with から omits such clauses.
So I think your original sentence omits “Don’t suspect me.” in front of that; “Don’t suspect me because I didn’t steal it.”
I don’t know if you can say “Because I didn’t steal it.” alone in English in this case, but that’s my interpretation.