Even a clavichord has got a damping mechanism, which damps the sound of the string, when the key is released. And as far as we know, the normal touch on keyboard instruments in these days was non legato. So a clavichord player must take the action of his instrument into consideration when playing, in order to produce the effect of non-legato.
The clavichord doesn't have a damping mechanism, nor does it have hammers - trust me, I've got one [a clavichord, that is, not a damping mechanism - you can hear my instrument playing my own compositions via links on my composer's thread, if you're brave enough
]. The easiest way to see its workings is by diagram- let me try one - the dotted line represents the length of the string:
As you can see, only one end of the sounding length
of the string is pre-defined (by the bridge); the other end is in its unplayed state muffled by the strip of light lint-like cloth through which all the strings pass. Therefore, the string, if plucked, produces only a relatively pitchless tone. The tangent (not hammer) which strikes the string near the left hand end therefore performs a dual function - to vibrate the string, thus creating the sound, but also to become one end of the string's sounding length. The fact that the point of impact is therefore right at the end of the string explains why a clavichord can only ever be a quiet instrument.
It should be noted also that the tangent is directly fixed to the end of the key and so, much more than a piano or harpsichord, where there is a mechanism in between, acts as a direct extension of the finger - if the finger shakes up and down, then so does the tangent, imparting vibrato (bebung) or even (though it's difficult to do) meaning one can bend the pitch of one not into an adjacent one, portamento-style. More importantly - the previous being only special effects and rarely used - the string will in theory continue to sound as long as the finger presses the key. In practice, however, the rate of decay is very fast and the sustain is therefore brief, which is why the clavichord can sometimes, especially in faster pieces, sound almost plucked.
No damping is required to prevent sympathetic vibration because, being only partially defined when unplayed, the strings will not vibrate. And no damping is required to stop the sound after the finger is released because as soon as the tangent leaves the string, the string reverts to its undefined state and stops ringing.