Do you think the new resistor could have affected the string so that a new resistor got damaged?
I doubt it, the resistor strings look like theirthey're part of different circuits. If the resistor did open, then it was most likely from heat. Each string appears to share the same trace (it looks like in each string the resistors are in series and each string is independent). This means each string has 5 resistors in series. If the resistors are in series and the same value, they should have mostly the same voltage across them and dissipate the same power.
If they died a heat death, then it could have been almost any resistor in the string, if the strings are independent then there is no relation between the death of the resistor circled in white or red.