If the following conditions are true:

1. Your "external machine" truly does have an open-collector output, and that transistor is working normally

2. The emitter of that same transistor is connected to ground

3. You have a 10kΩ resistance between collector and +3.3V

4. The only other thing connected to the collector is a *working* XOR gate input

then you absolutely should have a collector potential that goes between almost-ground (about 0.1V) and +3.3V.

So if you don't see those two possible conditions, then one of the above things is false.

With the collector potential clamped to a maximum of 0.6V, I suspect input protection diodes of the XOR gate are clamping the signal to ground. That would happen if the power supply (Vdd/Vcc) to the 74'86 IC is 0V, or broken or intermittent. Check that the Vdd/Vcc pin of the XOR IC is at least +3V.