A 4(5)-band resistor with an extra black band
Summary: I suspect it is a 20Ω 5% tolerance wirewound resistor - analysis below.




  I need to replace a burned resistor in an electric kettle


It would help to know what function this resistor had in the kettle. It's obviously a power resistor, but where was it connected? What was it doing? It wasn't in series with the element, if I'm correct that its value is 20Ω.


  My main question: What's the value of the resistor?



I believe the most likely interpretation, is as a 4-band colour code, with the black ring possibly indicating a non-inductive wirewound construction, but more likely just to mark the right-hand end.

Notice how the black band is in the middle of the end cap, whereas the red band (other end) is closer to the body of the resistor, making the black band the "odd one out", as expected for being the "right-hand end" of the markings.

Another indicator of the black band not being part of the value is, as kindly commented by StainlessSteelRat, band 2 cannot be gold. So the black end band is not part of the value.
So what is the value? I don't believe the (now) grey bands 2 &amp; 3 were originally grey. I suspect they were originally black. That makes sense, because value 20 (red, black) is valid in the cheap &amp; common E24 value range and since E24 range resistors are usually 5% tolerance, that makes sense with the gold band.

A grey 3rd band on a 4-band resistor would mean a very large (x100M) multiplier, which seems unlikely in a power resistor as seen in the photo. Also red, grey, grey (2, 8, 8) on a 5-band resistor isn't a valid value in any of the E-series ranges. These and several other reasons suggest that the original value was not red, grey, grey.

Therefore I suspect the original colour code (before heat affected the colour of bands 2 &amp; 3) was actually:

red (2), black (0), black (x1), gold (5%) i.e. 20Ω 5% tolerance 
I think I can see the subtle ridges of a wirewound construction in the photo. But why would there be a non-wirewound resistor in a kettle, which usually has a wirewound heater? Why avoid using a normal, inductive, wirewound resistor?

This goes back to the first point above - it would help to know what the resistor was doing, to guide the interpretation of the back band as either non-inductive wirewound, or just to mark the right-hand end.



  My follow-up question: Can a resistor have no tolerance?


No.

A couple of other points which weren't in your question:


What is the power rating of that resistor?

To decide that, you need to measure the existing resistor and try to match its size to other wirewound resistors, using one of the well-known distributor websites.
Why did that resistor fail?

If you don't find &amp; fix the cause, then any replacement is also likely to fail. It will help to start by finding what function that resistor has in the kettle.