Invalid tie in a repeat causes missed notes in MIDI

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I have the following code.

music = \relative c' {
    c4 e g e~
    \repeat volta 2 {
        e1
        c4 f a f~
    }
}

\score {
    \new PianoStaff <<
        \set PianoStaff.midiInstrument = "acoustic grand"

        \new Staff {
            \tempo 4 = 120
            \unfoldRepeats {
                \music
            }
        }
    >>
    \midi { }
    \layout { }
}

It can be seen that the tie f~ in the end of the repeat loop is
invalid since the next note after f~ is e1. When I play the midi, it
plays something like:

c4 e g e~
e1
c4 f a f
e1
c4 r a,4 f

You can see that in the last bar, c4 r a,4 f is played instead of c4 f
a f. In other words, the MIDI output misses the second note in the
last bar.

In the PDF layout however, we have the correct notes for the last bar:
c4 f a f. Could someone please explain why this difference between
MIDI and PDF layout?