After watching these two videos:
I made the oscillator described there, except that I used 74HC14, since I couldn't easily find the AC version.
For those who can't be bothered to watch the videos, it's a hex Schmitt inverter with an oscillator made from one inverter, 6.8 kilohm resistor and 4.7 nanofarad capacitopr. Its output is connected to the five remaining inputs. Those inputs are connected to female BNC connector via 220 ohm resistors. Schematic is attached.
Anyway, to the problem: It worked fine for a while and I was getting 5 V square wave of around 44 kHz with a 2.3 ns rise time and a volt or so of undershoot and overshoot. I could nicely see the reflection from the far end of coaxial cables I experimented with. Then I decided to take a look at how the signal would look like if I connected it directly to scope using only a coaxial cable. After I made the connection turned on the oscillator, it worked for a few seconds and then I lost the wave. I also noticed that current consumption increased a bit at that time.
After testing it out for a few minutes, I noticed that I'm getting a sinusoidal signal of around 600 mVpp and frequency going from 60 MHz to 62 MHz. After some probing, it turns out that pin 5Y is reading 75 ohms to the ground. Now that I disconnected the output resistor from it, I'm getting around 65 MHz at 8 Vpp. The signal is still sinusoidal and it has slow rise time of around 5.2 ns. It's interesting that the capacitor which I've used for the original oscillator now has no effect on the behavior of the circuit. Even if I remove it, the oscillations remain. Also I can affect the period a little bit by touching the chip itself.
Obviously the chip is dead, but I really have no idea what could have killed it. I mean, the scope has input resistance of 1 megohm and for its capacitance, there are the resistors on the output pins which should have stopped any big currents. Also all of my previous projects with 74xx chips worked fine, so any pointers on how to debug this would be appreciated.