The adapter is for an Android TV box, input 100-240VAC 50/60Hz 0.3A, output 5V 2A. The item was in use for about four years.
There is no screw; there is a seam, but it is glue together. So we cut it open. There is no obvious sign of damage. The resistance across the output terminals is about 22Ω. One of the output capacitors, 1000uF/10V, seems to bulge a little on the top. But after removing this capacitor, the resistance remain the same. It is eventually found that the diode D4 is the culprit; this diode is across the output, so it is probably a 5.6V Zener. The capacitor is also out of spec, measured only 28uF with 30Ω ESR. The capacitor is 8mm diameter and 14mm height rated for -40 to 105C, claiming low ESR. The capacitors of this spec is not common, probably among the smallest for this capacitance and voltage rating. Then the possible cause of the failure is the Zener damaged by the output over-voltage, maybe because of the output capacitor failure.
The controller IC is DP3733E made by Developer Microelectronics (深圳市德普微电子有限公司) and the datasheet is readily available online (although the company website has very little technical information). According to the data code, it is made in March 2019. The circuitry is close to the typical application circuit shown on the datasheet: a flyback controller with primary side regulation. The voltage feedback resistor divider 13KΩ and 2.1KΩ and a pair of parallel 1.30Ω resistors for current sensing. The difference is that there is a output LC filter but no input Pi filter. DP3733E features a high voltage BJT switch and a technique of quasi-resonant switching. The output voltage is sensed through an auxiliary transformer winding, no opto-coupler. After the BJT is turned off, the secondary starts to conduct. The output voltage is sensed as the current drops to zero on the auxiliary winding, which also starts to oscillate. The BJT is turned on when the valley of the oscillation is detected (it is a little more sophisticated than this as it also takes into account of the loading). This is the secondary waveform.
The flyback transformer inductances measured in circuit are Ls = 6.3uH, Lp=1.06mH, La=37uH. Perhaps, 13:1 turn ratio between the primary and the secondary and 1:2.5 between the secondary and the auxiliary.
At 5Ω load, the RMS voltage over the 10Ω is 0.92V. The efficiency is 45%.