This is the end of Leo Brouwer's study 4 from the "Estudios Sencillos":
Some notes here are tied to rests, or so it seems. What did Brouwer want the performer to do?
It means to let the chords ring, rather than cutting them off at the moment of the rest. Brouwer doesn't want the chords cut off; rather he wants them to fade naturally. This is a fairly common way to notate that. Sometimes such "ties to rests" will be accompanied by "l.v." or "Laissez Vibrer" ("let vibrate").
Here is an example from Debussy's Prelude for Piano (Preludes, Book 2, Number 1), the final two measures. The half-note chords are allowed to ring, via the damper pedal, and decay naturally (i.e., with the dampers lifted), while the two final chords are played.
Depending upon the style of music, I would be inclined to interpret notes tied to rest as an invitation to hold notes beyond the indicated duration if, in a performer's judgment, such treatment would make the piece sound better on the particular instruments being used, and in the particular venue where the piece is being performed, than playing them precisely as marked.
In many cases, it may be desirable to have a slight "echo" of notes that are played in one measure persist into the next measure, but for the sound of such notes to be much quieter than the sound of notes played in the later measure. If a piece is being performed in a very resonant space, or on a piano whose dampers quench string vibrations relatively slowly, this may naturally happen even if notes are cut off precisely at the end of a measure. If the piece is played on a piano with very fast-acting dampers in an acoustically dry space, however, the start of the next measure may sound very "empty" if notes were cut off as written. Unless a piece is written for a very specific purpose, there's no way a compiler will be able to anticipate the acoustics of the places it will be performed, or the characteristics of the instruments of the instruments that will be used, but a performer who is using the actual instruments in the space would be far better able (perhaps in conjunction with other people sitting in the audience area) to judge such things.