Everything that physically exists has mass, but one big question that continues to baffle physicists is whether or not it's possible for an object to have negative mass.
It may be possible for an object to have negative mass, but there are certain expectations matter must meet to have this quality: for one, it would have to be a perfect liquid, which has yet to be discovered.
Negative mass could theoretically exist because it doesn't defy the laws of physics or general relativity. Many laws of physics would still impact an object with negative mass and it could have momentum, on the other hand, it would defy Newton's third law.
What this means is if a negative object was moving in a particular direction, it would be moving opposite to the force applied; in other words, if you pushed said object away from you, it would move toward you.
Additionally, positive and negative mass objects would behave very strangely alongside one another, as the positive mass object would be repelled by the negative mass object, while the negative mass object would be attracted to the positive mass object, so it would be an endless matter chase.
Negative mass has never been proven, but it has been "theoretically" demonstrated under imperfect conditions. Nevertheless, it's still something we don't fully understand, but hope to one day unlock the secrets of.