I recently listened to a piano piece which contains headless notes.
The piece is Invocación a San Gregorio for Piano (2013) by Marco Alejandro Gil.
What is the meaning of this notation?
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The absence of noteheads may also be used to represent ad libitum pitch choices — a performance note can specify free pitch/vary pitch at will, and so on. (Elaine Gould, Behind Bars, p. 160)
The arpeggios are performed improvisationally, so the headless notes are there to mark the overall timing and the alignment with the melody but at the same time to indicate to the performer that the specific notes are improvised. This is demonstrated in the recording provided, where one can hear that the performed notes do not correspond directly to the notation but follow its overall shape.
Note the Spanish instructions below the arpeggios:
el orden, velocidad y extensión del arpegio puede variar mientras se respete la armonia.
the order, speed and extension of the arpeggio can vary as long as the harmony is respected.