I think Bethesda owns the IP for the Fallout franchise since 3. Sometimes companies just license out sequels to another development studio.
Obsidian has made many sequels to popular RPGs from other developers like KotOR 2 (Bioware made KotOR) and Neverwinter Nights 2 (Bioware made Neverwinter Nights).
Obsidian also makes games based on it's own original IP like Pillars of Eternity, Alpha Protocol, Tyranny, etc. It's a great studio with lots of fun games!