No, variations do not survive. Variations that are not suitable or advantageous to the organism in the prevailing environmental conditions are not maintained. Environmental factors act on these variants and the variant most suited to the existing environment would survive.

In asexually reproducing organisms variation occurs due to inaccuracies in DNA copying at the time of nuclear division.
For example, one bacterium divides, it will give rise to two bacteria. These daughter bacteria would be similar in body design, but with subtle differences. The resultant bacteria divide again, and each bacterium will give rise to two bacteria in the next generation i.e., there would be four individuals

Fig. Appearance of variations over succeeding generations
The four individuals will be different from each other. They may have differences of two types (i) some of the unique type of differences and (ii) differences inherited from, their respective parents, who were different from each other.

Trait B may have arisen earlier as it is present in more members of the population. It must have arisen earlier and has now spread to 60% of the population. Whereas trait A must be new as it has spread to only 10% of the population.

The variations ensure that the survival of the species as they allow the members of population to adapt to the changing environment and conditions. The species are more suitable to the changed environment . Thus continuity of the species is maintained.
For example, Bacteria variants which can withstand tolerate heat will survive better in a heat wave than variant which cannot heat wave. It proves that creation of variations in a species promote survival.