I won't quote a rulebook as you haven't specified a ruleset, but the rules are fairly consistent (and well known). Once you specify which rules you play under I can find the rule quote. One example is from the National Softball Association rules, Section 8c.
The first runner to occupy a base is entitled to that base legally. The second runner is not protected by that base. The trailing runner is not automatically out, however, so long as they do not pass the lead runner. If they are still in the right order, then both are still 'safe' until put out by a tag or a force.
As such, the question here is largely one of what happened with the fielded ball. Assuming the runners did not pass out of order, then, and both are physically touching second base, the following are possibilities:
The base was tagged first. If that is the case, the runner from first is out. The runner from second then is no longer forced and can stay on the base.
The runner from first was tagged first. Same as above - the runner from second is no longer forced and is entitled to stay on his base.
The runner from second was tagged first. Then, the runner from second is out (as it is a force play); the runner from first is then entitled to the base as the only not-out runner and may stay on the base.
None of these end up with a double play, you'll note; a runner always ends up on second base. The only way a double play would have been possible is if the runner from first had not touched the base; then it would be a force, assuming the fielder tagged the runner from second AND the base itself (just tagging the runner is not sufficient).
So, if the runner from first was in contact with the base, and the first action on the part of the fielder was to tag the runner from second (prior to touching the base with his/her foot), then the runner from second is out, and the runner from first is safe.