There was a moratorium during the war at one point within the Royal Navy telling captains not to ram U-boats after some bad events where ships were either heavily damaged or even sunk because of it. One book I read recently the captain of an escort, HMS Hesperus, rammed a U-boat but was left with massive forward damage. The keel of the ship was actually crumpled back a fair bit causing flooding and left the ship stationary for some time until the damage could be sufficiently repaired to allow for forward movement. So it is possible for a DD to be sunk by the ramming of a U-boat though it isn't likely to happen without the U-boat also going down.
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