Character death untags "player", and tags "dead" and "dead player".
When rejoining, the dead character will somehow have regained the "player" tag, but still also have "dead" and "dead player".
The check in Crate.as getPlayerInside() can be changed accordingly.

There will be a normal inventory button, but it will not present an inventory for some strange reason,
even though isInventoryAccessible() returns true and GetButtonsFor() doesn't interfere in any way,
as long as the dead character is inside.

Maybe the inventory button (which is handled engine side) has some additional failsafes that disables the inventory if it thinks an alive player is inside?

I figured it out just after my previous post.
It looks like I was right. When the character doesn't have the "player" tag, the inventory can be accessed.

It requires changing

this.tag("player")

to

	if (!this.hasTag("dead"))
		this.Tag("player");

in all runner blob init functions.
I will fix it soon.