In baseball if a play ends and two base runners are at the same base who is safe and who is out? Does the situation change if one of the runners can be forced?
Technically the play cannot end with two runners on the same base.
If two runners are occupying the same base, then the trailing runner is considered "In Jeopardy", or able to be tagged out, and must either retreat to the previous base or, if it is occupied, the leading runner must advance a base.
However, if the trailing runner was forced to the base then the leading runner is considered "In Jeopardy" and must advance or be tagged out.
According to the Official Baseball Rules posted on MLB.com, rule 7.03 states:
(a) Two runners may not occupy a base, but if, while the ball is alive, two runners are touching a base, the following runner shall be out when tagged and the preceding runner is entitled to the base, unless Rule 7.03(b) applies.
(b) If a runner is forced to advance by reason of the batter becoming a runner and two runners are touching a base to which the following runner is forced, the following runner is entitled to the base and the preceding runner shall be out when tagged or when a fielder possesses the ball and touches the base to which such preceding runner is forced.
My interpretation is that the following runner will be out in this situation unless he/she was the hitter and was advancing to a base - in that situation, the preceding runner needs to advance or will be tagged out.