I have done projects with some strips as narrow as 1/4".
I place a wide board, same thickness as the strips I am saving, under the guide bar and place the narrow edge i am saving between the wide board and the blade. As Eli has stated, i place a narrow sacrificial piece in crosscut position at end of the piece i am cutting. I sometimes clamp a straight piece aganst the off side of the piece I am cutting. This piece, I keep moving in as the piece i am cutting keeps moving towards the blade.
I don't have t put any pressure against the piece I keep moving. It just has to fit against.
If I don't use the sacrificial piece at end of cut, i will have a search and find project as the saw finishes the cut. A lot of times, i may be just cutting a wide board with a thin strip being cut off. If the board is short, i use the sacrificial cross cut board to keep the off cut from flying into space. In that case, I clamp the off cut end of the sacrificial piece while the section under the board gets thrown away after the first cut. In my shop, a flying piece might still be close by as the wall is only about 3 feet from the end of the cut. That piece has never come close to coming back to bite me [scared], but whatever it might collide with, the noise can be quite scary. The Festoy system of guide bar, saw and clamping devices does have the tendency of making the small shop a much safer place to be if one makes use of all parts to the "system".
Tinker