If you split the phrase u want. Select that clip after splitting then right click and select "bounce to clip(s)" this will essentially cut out all the audio data not shown on the clip so u can extend that clip out into silence to be lengthy enough for any echo or stutter or effect u want.I've ran into the situation u mentioned multiple times and found this is easiest way to do it.
As u probably know, simply adding an echo to that clip or whatever will end when the clip ends, by doing the bounce to clip trick it no longer contains the rest of the data beyond the clip extension. (So only part u want is there). This will allow u to extend out long enough for the effect u want.
In short... Split phrase or word you want/select that split clip/right click, select "bounce to clip(s)"/add effect and extend out as long as u like to accomadate.
This will also allow to keep everything on the same track.