Broken Paddle (paddle clamp breaks, blade is damaged or falls off)
You may prepare yourself for breaking your paddle by practicing paddling with half your paddle. Store half your paddle on your aft deck and paddle with the other half. Practice in progressively rougher water
Swimming - practice can help you determine what techniques are most effective under various conditions. You may have to abandon your paddle also in order to swim more effectively if there is little or no prospect for recovering your boat.
with paddle
If you are very bouyant (such as when you are wearing a dry suit) You can float on your back and back stroke with your paddle
Or hold your paddle just below the blade and point it in front of you and swim with your other hand.