The simplest answer is probably that there is a cavity in the object that is filled with air. As the pressure is reduced, the air can expand. This changes the volume of the object slightly, until it's sufficiently large that the weight of the displaced liquid is greater than the weight of the object.
If the object does not change size, this effect could not occur. Water is almost incompressible: and if it was compressible, it would get less dense as the pressure above it decreases. This would mean that the weight of the displaced liquid would decrease.
There is a similar well-known experiment I did as a child with a piece of orange peel: if you add just the right amount of weight to it so it barely floats, and you put it in a closed plastic bottle, then you can squeeze the bottle and cause your "submarine" to sink (because air pockets in the peel are compressed).