If you undergo ketosis your fat cells will be lysed. Anecdotal reports aside, physiologically that must happen unless you are incapable of it (a genetic mutation which would - speculatively - have far-ranging effects).

Why must that happen? Ketosis means that lipolysis is occuring. Lipolysis does not inherently require that fat cells must be lysed as a physiological inevitability. ie. The fat that is to be broken down can itself come from diet instead of the lysing of fat cells.