No battery should ever get fully discharged. Deep cycle batteries have thicker cells, deeper cases to prevent shorting, and a couple other differences from 'starting' batteries, but even they cannot handle a full discharge without damage. They are designed to be able to withstand many more cycles and recharges, but you still have to keep them above about %20 at a minimum. Always read the literature for your particular battery to be safe - failure to know what you have and treat it properly will lead to early/sudden failures.
- R