Is a chemical property of a base is that they crumble?

No,

Crumbling, or perhaps a more scientific term would be brittleness would be a physical property of a base.

I.E. it would be one of the properties that you can observe by looking at the base in isolation.

Chemical properties are how they react with other chemicals. One definition of a base is a "Proton (or Hydrogen Ion) Acceptor", and an acid is the opposite, a Proton (or Hydrogen Ion) Donor". Acids and bases, of course, are very reactive with each other, and may even be reactive in water. They can also eat away or corrode many materials including metals.

Thinking of brittleness.. some of the bases you would encounter are found in salt forms when anhydrous or without water. For example Sodium Bicarbonate, Sodium Hydroxide, Potassium Hydroxide. All these forms are ionic bonded, and would tend to form brittle crystals somewhat like salt (NaCl).

This may be true of most bases in that the majority of the bases essentially have substituted one of their hydrogen atoms for a Sodium, Potassium, Calcium, or similar electropositive ion.. This, however, is not universal. One notable exception is Ammonia. It's form, NH3 is basic, and it happens to be a gas at room temperature, and must be either cooled or pressurized to make it into a liquid. It's conjugate acid form (Ammonium, NH4+) is the ionic form. It only becomes a solid at -196°C.