Can you give a sketch of your system? The problem is not very clearly defined in words.

No matter whether the rubber string looses energy through impact with the wood, through friction with the wood or air drag, simple vibration of the string will itself cause loss of energy.

The string would loose energy due to internal friction called material damping. For a simple experiment, take a rubber band and try to pull and release it a few times in quick succession. You will see that the rubber has heated up. That happens due to material damping. Of course, this is a simple explanation. The physics related to rubbers which show hyper-elasticity or pseudo-elasticity can be very complex: see Mullins effect, hysteresis curves, stress softening, etc. for example.

Thus, due to internal damping alone (forget friction, impact, air drag etc.) , the rubber string will eventually stop, even in vacuum and with zero external friction.

In other terms the string will stop due to its so called viscoelastic baheviour. This is defined as the E' and E". E' is the elastic modulus or storage modulus and E" is called the loss modulus. The loss modulus causes damping, due to conversion of energy into heat (see above) - that is a loss of energy.

Rubber strings are made of polymers with very long chain cross-linked molecules. With oscillations, these cross linking break and reattach continually. Each time a cross link is broken some amount of energy is lost. This shows off as material damping (heating) or so to say the visco-hyper-elastic behavior in the material as a continuum.

Since every material has some damping associated with it, which accounts for internal friction leading to dissipation of energy from the system. The only notable outcome from your experiment would be that since there is no medium (surrounding rubber) to get disturbed there wont be any sound generated..

so all of you want to say that the energy of rubber tension will convert into heat due to friction or damping and then by the radiation process that energy will be lost by the system and finally rubber string will come to rest right??

so thanks to all of you for solving this problem and involving yourself in this problem.