The Collector is still alive after the events of Avengers: Infinity War.
In The Guardians of the Galaxy Holiday Special (2022), it is revealed that the Guardians of the Galaxy purchased Knowhere from the Collector, and are in the process of refurbishing it (emphasis mine):
Nebula: Ever since buying Knowhere from The Collector, we don't have time for trivialities like Christmas. This place needs a lot of fixing up before it's livable.
James Gunn (director of Guardians of the Galaxy Vols. 1-3) confirms the same (emphasis mine):
Although the Guardians are sometimes heroes, they work as mercenaries & it brings in a fair amount of money. So after Thanos attacked Knowhere they bought it from the Collector. It was a burnt out husk & they’ve been rebuilding it.
- @JamesGunn tweet
They've bought Knowhere from The Collector, that's their home base now -- all of those things are important to Vol. 3.
- James Gunn Talks 'Guardians of the Galaxy Vol. 3' and His Future With Marvel (Exclusive). Entertainment Tonight
The Collector has never been confirmed to be dead after Infinity War. Nebula and James Gunn said that the GotG bought Knowhere from the Collector directly, and not from his heirs or someone else, implying that the Collector is still alive to consent to the transaction. A dead man can't sell his possessions, since he can't consent to the transaction.