The law of conservation of mass, also known as the principle of mass/matter conservation, is that the mass of a closed system (in the sense of a completely closed system) will remain constant over time. What this means is that the mass of an isolated system cannot be changed as a result of processes acting within the system. So the short answer to your question is the mass remains constant.
When one considers the conservation of matter, however, things tend to change a bit. The principle of matter conservation (in the sense of particles which are agreed to be "matter") may be considered as an approximate (not exact) physical law. This is true only in the classical sense, without lending consideration to special relativity or quantum mechanics. Another difficulty with matter is that it is not a well-defined word scientifically, and when particles which are composed of protons, neutrons, and electrons (matter) are annihilated to produce photons (not matter), this conservation most certainly does not take place.
Mass is conserved during a physical change. If you think about some examples, this makes a lot of sense. For instance, if you cut a piece of paper in half, you still have the same total mass of paper. Similarly, if you break a glass, you have not lost any of the glass' total mass. You simply changed the shape.