Supernovae are only one mechanism which can initiate the collapse of an interstellar cloud into creating stars, other causes could be responsible, among them normal gravitational contraction or even the passing of a density wave through the disk (the reason spiral arms are marked by very bright young hot blue giants).

Supernovae undoubtedly play some role, since many stars are formed as the cloud compresses, the heaviest will evolve rapidly and likely go SN soon, seeding the cloud with metals which could be incorporated into smaller, longer-lived stars later. My guess is that the cloud's chemical composition will evolve throughout the intital burst of star formation, constantly being modified by the SNs and stellar winds of the most massive, most quickly evolving stars.

After the resulting open cluster matures, these catastrophic events clear the gas and dust out of the area, stellar genesis halts, and the cluster gradually evaporates due to galactic tidal forces. Most of the resulting clusters we see are relatively young (< 0.5 Gy) and generally, the younger they are, the more interstellar medium they still have available. The more compact and gravitationally bound ones may survive to several Gyr, but as a rule, their stars are scattered and mix into the general disk population. At almost 5 Gyr of age, our Sun has probably lost most of its siblings, they could be on the other side of the Galaxy by now.

Many of these sibling stars would have just drifted away, they might be identified by having low proper motions and low radial velocities relative to the Sun (they are traveling with us like a cloud of buckshot moving through space). But many would also have been energetically ejected by gravitational encounters with the surviving cluster members, and they'd be long gone by now. For that matter, we might have been slung out of the birth cluster this way too. To have survived as long as the Sun, they too would have to be small, faint stars (the life span of a star is inversely proportional to about the cube of its initial mass) and massive stars are both very bright and burn out quickly.

So what should we look for? Old (approx 4 to 5 Gyr) dwarfs who are relatively motionless with respect to us, and with similar (but not necessarily identical) similarities in isotopic abundances: a challenging, but not impossible observing program. But there would be no guarantee of success. Even if we found a few in the solar neighborhood, they might just be coincidental strays from some other cluster.