The suit IS a solid object. The nanites are sort of liquid-y when stored in the chest piece, but once out, they do solidify!
How else his suit supposed to function as armour, unless it is solid?
The key element of the nano-tech is that the nanites can flow like a liquid, and then solidify once they are in place.
About the "constituent parts" this is true either case. When he suits up for the first time in Infinity war, we can see the nanites form the constituent parts layer by layer as the suit builds up around him. They have taken the time to specifically show this.
The image below clearly shows the sut being composed of multiple layers, parts and components just like all other suits:
Also, his suit can form solid constructs that are not directly attached to the suit:
So in summation, the suit is always solid and made of constituent parts. It doesn't have to be dead to turn solid.
Some further info based on some question from the comments:
His helmet looks damaged despite being a nano-tech thing, is because he has barely enough nanites left to actually heal it.
On Titan, he uses up a vast amount of nanites while battling Thanos. So much so that at one point he has no armour on his legs and half his face.
He then uses up some nanites to fix his stab wound.
This means that by the time we see that scene in Endgame, he must be running just as low on nanites as they were running low on Oxygen!