In my field, we often supervise students for internships. Myself, and my two collegues each have students from different schools, who are taking approximately the same class.
S1 asked S2 if she could read her paper on a proposal. S2 said "sure" all about helping out another intern. S1 asked if she could make a copy, and S2 said "I'm afraid that won't be possible, but you can read it over." S1 said that she couldn't possibly read it today, and she really needed a copy. S2's instructor, (my collegue who is normally a pushover, but I'm proud of her for this) said, "S2 is really uncomfortable with giving out copies of her paper, it has taken two weeks for her to write it, and she is not done. She would happily let you read it over today or next week."
Plagerism alarm bells going off. S1 then approached S2 again and asked for a copy... AGAIN! She politely said no again, and came to me. She is now concerned that S1 made a secret copy.
My first thought is to approach S1's supervisor. Not being accusatory, but maybe asking him to talk to S1's prof, and forward a copy of S2's paper to the school. That way if it is innocent, no harm no foul. If it isn't, the school has proof of plagerism.