Shardblade wounds

[Steel Inquisitive he/him]

If your arm is cut by a shardblade it becomes lifeless. The person won't be able to move that arm in anyway. His soul no longer extends through his arm.

Now, what if after his arm has become "dead" he got a cut in that arm? Would it heal like normal? Or would he bleed to death?

[Calderis he/him]

It's still attached to the body. It's still living flesh as it doesn't rot, or Hobber would have died from sepsis. 

So I think it would function like a paralyzed limb. You can't move or feel it, but it would heal normally, but bloodless from a wound of which you're unaware is a real concern 

[RShara she/her]

I don't think it would heal or bleed. Everything in it is dead, as if it had actually been severed, so it's just an inert mass on the end of your shoulder, now.