Rhythm and texture have more to do with endings than the harmony. You can end a piece on any chord you want to, so long as you set it up right. With rhyhm, you can hold the chords longer at the end (whole notes, half notes) rather than continuously strumming them (typically eighth or sixteenth notes). With texture, you can have certain people in the band drop out, or you can play chords that are thinner (less notes), or in some situations do the exact opposite: keep building up and just abruptly stop. Another common tool to use is repetition. Try repeating the last chord or two, or last lyric, or add a quick riff to the end and repeat it a few times (three is always the magic number, from jokes to music, our brains seem to be geared to hear repetitions of three). Dig out some tunes you like listening to and figure out how they end the song, and take notes.