Several items in League of Legends grant additional gold per 10 seconds to the wielder. Does the extra gold bonus on these items work while you're dead and waiting to respawn?
I had always assumed that it did, but to make sure, I just tested two cases in a custom game. I did these tests on The Proving Grounds for convenience; the passive gold gain bonus on the map shouldn't affect the results.
In addition, I used Greater Quintessences of Avarice and full points in the Greed mastery for a total of +5 gold per 10 seconds.
I proceeded to purchase a Philosopher's Stone when the in-game clock read 1:00. From here, I did one of two things. In the first case, I cast Whimsy on myself whenever I was alive and ran directly to the Outer Turret. When the in-game clock hit 5:00, I had 1923 gold.
In the second case, after buying the Philosopher's Stone, I sat in my base until 5:00. At that point, I had 1917 gold.
The minor differences can be attributed to the inaccuracy of the client-side game clock.
In short, yes, gold per 10 items still tick while you're dead.