I looked with oscilloscope and If I understand correctly, it shows that positive side of the capacitor drops from 0.7 volts to about -7 volts. This negative voltage will obviously make transistors turn off. But why does this happen?The speaker is an inductor and in conjunction with the capacitor it will form a resonant circuit. Every time Q2 turns on it pulls the junction of the inductor and capacitor up to +9 Volts.

-7v will also cause breakdown of the base-emitter junction of Q1.This negative voltage will obviously make transistors turn off.
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I am still a beginner in electronics but to me this answer makes the most sense.It's all about the voltage on the base of Q1.
View attachment 329162
At startup, capacitor C1 is discharged. C1 begins to charge via R1.
When Q1 B-E voltage reaches about +0.7 V, Q1 conducts and turns on Q2 hard.
C1 is immediately charged to about +8 V while the base of Q1 remains around +0.7 V.
With Q1 now turned on, C1 and Q1 base node slowly discharges through the base-emitter junction.
When Q1 base-emitter voltage drops below +0.6 V, Q1 and Q2 turn off. This pushes Q1-C1 node to about -8 V.
Then the whole cycle starts over.
There are two time intervals at play.
1) The R1-C1 charging time where the base of Q1 has to go from -8V to +0.7 V.
2) The C1 discharge time where the base of Q1 has to fall from about +0.7 V to +0.6 V via the base-emitter current.
TEST CIRCUIT
Here is the test circuit I used to produce the oscilloscope waveforms. Note that the supply voltage is 5V.
View attachment 329164
Channel 1 is the voltage at C1 - R2.
Channel 2 is the waveform at C1 - Q1.
View attachment 329167
I wonder why Q1-C1 drops to -8v. Is it because C1 voltage difference was 0.7v - 9v = -8.3v. When 9 volts drops to 0 volts it tries to keep the same voltage difference of -8.3 volts? So 0.7 volts changes to -8.3 volts? Now it is -8.3v - 0v = -8.3v?With Q1 now turned on, C1 and Q1 base node slowly discharges through the base-emitter junction.
When Q1 base-emitter voltage drops below +0.6 V, Q1 and Q2 turn off. This pushes Q1-C1 node to about -8 V.