What are the drawbacks of using explosives?

I remember someone telling me in-game that using explosives (grenades, rockets, etc.) has some drawbacks, in that I get less "loot" after the mission. But it seems that all the aliens' weapons self-destruct anyway... so what are the drawbacks of using explosives?

In particular,

1. Does it mean I get less weapon fragments / Elerium / alloys?
2. Does it mean I no longer get the alien's corpse?
3. Can explosives kill neutralized enemies or destroy their weapons?

Also, if I use explosives to injure aliens but not kill them, do I still lose anything?

Solution 1:

When an alien dies from an explosion, you will still get the corpse, but you will be unable to acquire any of the other loot. If an alien is only injured by an explosion, then killed normally, you will get all the loot you normally would.

The alien's weapon self-destructing is what results in the weapon fragments you normally find. The explosions instead vaporize it entirely.

As @RavenDreamer said, stunned aliens can be killed by explosions, which will destroy their weapons.

Considering the danger of losing alloys and elerium (and also functional UFO hardware like flight computers and power sources) you might want to be careful with explosives on UFO raids, since you might destroy parts of the UFO when using explosives inside of it and lose this loot (which you might need to build stuff like Satellite Nexus or Elerium Generator).