TL;DR:
Either there's a problem with the head gasket, or with the piston rings.
Remember, the piston rings fly over the openings in the cylinder wall, and there's no radial force onto the section exposed to the opening, pushing it into its groove. Shortly after, this section touches the cylinder wall again and experiences the radial force pushing it back. Piston rings are rigid enough that this usually isn't a problem, but it is a weak point, and the piston ring may break there. If it breaks into more than two pieces, one may escape through the exhaust, leaving the motor with low compression.
How a 2-stroke motor works
This animation shows a 2-stroke motor at work:
(Source)
Let's go through the steps, staring with the ignition:
- The cylinder is in the upper position, there's already fresh mixture (green) at ambient pressure in the crank case, and the pressure from the combustion forces the piston down.
- At some point, the exhaust opening is uncovered, and the pressurized exhaust fumes (gray) leave the cylinder
- A little later, the intake opening is uncovered. The mixture in the crank case has been pressurized a little until now, because the reed valve prevented it from flowing back into the carburetor. The fresh gas is pushed into the cylinder, and helps to push out the exhaust fumes through the still uncovered exhaust opening.
- Well, that's interesting: The inertia of the moving exhaust fumes pulls in even more mixture directly through the carburetor! Some of the fresh gas even flows into the exhaust.
- The piston moves up and first covers the intake opening. From now on, new mixture is sucked into the crank case.
- Due to the special design of the exhaust system, the mixture in the exhaust is pushed back into the cylinder right before the exhaust opening is covered. This means, the mixture in the cylinder is already compressed a little at this point, though the effect heavily depends on RPM.
- When the exhaust opening is covered, the final compression in the cylinder takes place.
Compression
When the piston moves up, the pressure above increases a lot, somewhere into the region of 15-20bar (atmospheres). Since the reed valve is open at that moment, fresh mixture streams into the crank case, and it doesn't build up any noticeable vacuum. The force exerted by the pressure onto the piston is the (periodic) resistance you feel when starting the motor.
When the piston moves down, it indeed compresses the mixture in the crank case, but since the ratio of volume between piston up and piston down isn't that large, the max pressure in the crank case is not so high. Also the much higher pressure in the cylinder helps to compress the gas in the crank case. Due to this, you can hardly feel the resistance from this compression.
Also, at low RPM (i.e. when starting the motor) you can assume ambient pressure in the cylinder when it covers the exhaust opening, and the compression relies on the tightness of the piston ring, the head gasket, and the spark plug. So if you say there's no compression. i.e. no resistance, the problem should be located there.
Defect reed valve
The reed valve can become leaky. In this case, some air can go through the carburetor three times, leading to a way too rich mixture. And due to the lower pressure in the crank case, the exhaust fumes in the cylinder aren't replaced by mixture very well. As result, motor performance is low, especially at low RPM where more mixture can escape through the valve. Depending on how bad it is, the motor even will not start. But you will not notice that as low compression!
The reed valve can also break, but then you have debris flying around in the motor, making even more damage.
Repair
You can check the reed valve if you want, it sits directly in the wall of the crank case wall, and should be easy to remove.Judging if it's OK or not can be difficult, though.
I'd definitely disassemble cylinder head, cylinder and the piston to check the rings / condition of the rest. It's not that complicated if you dare to do it. The most important things are not to let anything fall into the crank case (cover with cloth) and being careful when pushing the piston back into the cylinder, since getting the rings in is a little tricky.
