Need help finding a proper replacement for a burnt resistor
(I'm assuming that you cannot just measure the value of the resistor with a multimeter i.e. it has failed &quot;open circuit&quot;.)
Resistor value
Based on the photo, my initial hypothesis is that the relevant colors are:

Brown
Black
Gold (not Brown)
Silver

meaning 1.0 Ω, 10% tolerance
The yellow on the end cap will have a special meaning, as already commented - perhaps something about the functionality (e.g. fusible).
Investigate
Since you don't have a schematic, I would reverse-engineer that part of the circuit - I see a relay and what could be a TVS and another SMD component nearby. Identify the function of that resistor in the circuit, and that will help give a clue about whether a 1 ohm value is reasonable or not.
Danger!
For that resistor to have failed open-circuit likely means that you have a fault elsewhere and that resistor is just a victim. Indeed, it does not seem to be very burned, yet it has failed. That give a big clue that the resistor may be a fusible type, which is specifically designed to fail when overloaded.
That would also suggest that any replacement resistor (a) must be the correct value, but also (b) must be of the same fusible type. Using a normal resistor in place of a fusible resistor can create a risk of fire in the event of a fault (and therefore potentially causing damage, injury or death). You will often see warnings on (good!) schematics for fusible resistors, stating that they must be replaced by an exact part number (i.e. an identical fusible resistor).
Therefore you need to be very cautious when replacing that resistor, to ensure that you don't introduce a safety risk which could later cause damage, injury or death.

From your comment:

a TNY264GN chip is also blown

They are a common failure in products which use them. FYI, in this previous question with a failed TNY264, the OP reported a 2.2 Ω fusible resistor was used in their (different) product. Therefore my hypothesis of the resistor value being 1 Ω is in the same order of magnitude.