Han Solo's death came long after Chewbacca pledged a life debt to him, and Chewbacca remained his devoted partner for many years.
A life debt represented a social convention where an individual was obligated to repay someone who had saved their life. The Gungans and the Wookiees were two cultures that notably practiced this custom.
Qui-Gon Jinn invoked a life debt concerning Jar Jar Binks to prevent Boss Nass from punishing him for returning to Otoh Gunga after his banishment. Jinn wanted to keep Jar Jar around to guide him on Naboo.
Ezra Bridger constantly reminded Garazeb Orrelios that he saved him from an Imperial agent. Because of this, Ezra pointed out that some cultures dictated that a person becomes the servant of the one who saved their life. Zeb was unimpressed and told Ezra to leave. Later, Ezra tried to act like Zeb owed him a life debt, complaining about Zeb making him carry supplies after Ezra saved Zeb's life. After this, Zeb rescued Ezra from pursuing Imperials and declared that any perceived life debt was now void, since they were even.
Chewbacca swore a Wookiee life debt to Han Solo on Mimban because Solo freed him from captivity under the Galactic Empire. After bounty hunter Boba Fett saved Mercenary Fennec Shand in the deserts of Tatooine, she pledged a life debt to him. She quickly repaid her debt, but she decided to stay with Fett and helped him build a new criminal empire. In the Smuggler's Guide, Solo joked that if Chewbacca ever took another life debt after Solo died, Solo would haunt him through the Force after recovering the Millennium Falcon.