Enzymes that break down dna catalyze the hydrolysis of the covalent bonds that join nucleotides together. What would happen to dna molecules treated with these enzymes?

The phosphodiester bonds of the polynucleotide backbone in DNA would be broken.

The phosphate of one nucleotide is covalently bound to the sugar of the next nucleotide in DNA molecule (or hydroxyl groups in phosphoric acid react with hydroxyl groups on 3' carbon atom of one sugar molecule (deoxyribose) and the 5' carbon atom of another sugar molecule (deoxyribose) to form two ester bonds).

Hydrolysis of phosphodiester bonds is catalyzed by the action of enzymes phosphodiesterases.