IC that would pull output to the ground, perhaps NOT gate?
The fact that relays are actuating at reset when pins should be in a high impedance mode is worrisome, and something that you need to fully understand in order to validate your system and fix it.

Edit: now that it is clear that this is a software bug in your code, to solve the inadvertent drive low during starting, configure the pin's output data register bit to high before you set the pin to be an output.

That said, a literal answer to your original question would be a chip containing several open collector inverters.

The 74xx05 is an example.

The 74xx06 is similar but allows applying acceptable voltage to the output even when this exceeds the supply voltage, for example you can operate the part on 3.3v but pull down outputs from 5v.

But these are not the solution to your actual problem.