[Hanuman]

The few Meg-Ohms reading will be the open circuit, and what you are actually reading is probably just the total circuit impedance itself. There’s more than just coil and contacts inside some of these.

The few hundred K-Ohms is quite possibly damaged/welded but dirty contacts. Very high resistance. If this is one of those relays with a metal case, slightly crimped on, for fun you could open it, and have a look. Some fine emery or wet-dry could clean the contacts.

I say could. It’s also probable that a circuit component such as a capacitor has actually failed. Arcing across contacts will recur.