As for Carbon comp resistors, yes they drift but they were probably not selected for their precision nor stability. But if they cooked the board, it might be a good idea to install bigger one and try to distance them from the PCB.
Possibly selected for their ability to survive short-term overload - which might be relevant if they are torched!
From TAoE 3 p1105
C.4 Resistor types
The usual choices for general-purpose use are metal-film
(axial-lead) or thick-film (surface-mount) parts. Thin-film
surface-mount resistors offer improved characteristics (ac-
curacy, stability, and ability to operate in cryogenic envi-
ronments). For power applications you usually use wire-
wound resistors, either in an air-cooled ceramic package or
a conduction-cooled (“Dale-type”) metal package. High-
value resistors (>10 MΩ, say) are usually of metal-oxide
construction (e.g., Ohmite “Mini-Mox” or “Super Mox,” or
Vishay RNX-series).
Film resistors are not tolerant of high
peak power; for such applications use something like ce-
ramic or carbon composition, or other styles specified for
peak-power use. For the utmost in stability and low tem-
perature coefficient (tempco), you can’t beat the excellent
metal-foil types from Vishay. They exploit a clever design,
in which the positive tempco of the resistive metal element
(firmly attached to an insulating substrate) is cancelled by
the negative strain-induced tempco caused by differential
expansion of the substrate.3 We’ve listed some compara-
tive resistor properties in Table C.1; for much more detail
see §1x.2.