What is a state of matter that has fixed shape but not fixed volume?

Answer 1

This question seems to have been asked in the reverse order. It is far more likely that someone interested in the subject would ask, "What is the state of matter that has fixed volume but not fixed shape?" The answer to that question is "incompressible". Incompressible means constant in volume despite changes in pressure. A body of water is incompressible but can change shape. We change the shape of a glass of water by drinking it, but we don't change its volume. The matter which fits this "reverse question" is the incompressible fluid (or incompressible flexible solid).
To satisfy the question asked, the "thing" has to expand or contract at the same rate in all directions. A cube of material with side length of a metre might expand and become a cube of 1.5 metre side length. It is still a cube but of greater volume. A bubble or balloon which expands or contracts because of a change of temperature or pressure is a valid example. However, "being" a cube or a balloon is not a "state" of matter. It is a contrivance and more a result of its history rather than a state of its material.

Answer 2

Liquid, and if contained, gas

Answer 3

Liquid. :)