The standing wave on the string creates a travelling pressure wave in the air around the string, i.e. sound. (In a real musical instrument, the mechanism of sound production is a little different, but the concept remains the same. See @Hilmar 's comment on this answer.) This carries away energy and damps the oscillation on the string. Hence, the standing wave will decay; to maintain the standing wave on the string, you must drive the oscillation, through a method like pulling a bow across the string or repeatedly plucking the string.
The principle of superposition tells us that if two waves $\psi_1$ and $\psi_2$ are allowed on the string (satisfies boundary conditions), any linear combination of them $c_1\psi_1+c_2\psi_2$ will also be allowed on the string. So, in real life, the standing wave on a string can be decomposed as a harmonic series, i.e. it is a linear combination of the pure harmonics. Typically, the fundamental frequency determines the pitch, and the smaller contributions at higher harmonics determine the timbre (tone quality).