How can I tell if a pencil's core is already damaged?
Often you can't, until it breaks on sharpening. If a pencil has been left in a hot car, on a sunny windowsill, or in a warm bag for an extended period, treat it as at-risk even if it looks fine from the outside.
Can a cracked pencil be saved?
For wax-core colour pencils, yes - try the wax heat-fusion method above. Graphite pencils can't be repaired this way; a pencil extender is the better option once they're too short or damaged to sharpen further.
Does this apply to every pencil brand?
Yes - wax-core sensitivity applies to most colour pencils, including Stockmar, Lyra Super Ferby, and Colour Giants. Graphite pencils are more heat-resistant, but their wooden casing can still warp, so the same storage habits are worth following regardless of brand.
Remember:
A little care in storage and sharpening goes a long way. The same handful of habits -out of the sun, flat in the tin, a sharp blade, and a bit of patience with hot pencils - will keep almost any pencil collection performing well for years.