A resistor is a straight resistance where the speaker is an impedance, meaning that it's resistance varies depending on frequency.
Be sure to be very careful with terms.
The speaker
has impedance, so its
reactance varies with frequency. As reactance increases, the
impedance will also increase, as impedance is the vector sum of resistance and reactance.
So what I'm saying with this is the
resistance itself doesn't change, even though the total impedance will.
... but what happens when the resistance of the speaker rises at certian frequencies? ...
The total impedance will rise somewhat, which will be less apparent if all loads are in parallel. Try it out: calculate the total load of four 16Ω resistors in parallel, and four 4Ω resistors in series; recalculate for each situation assuming one of the resistors is now 4x as big.
My main concern for asking was is there a risk of damage?
If you want to go down this road, you'll need to research "real power" vs. "reactive power" (and the related term "power factor").
Bottom line: heat dissipated only results from the "real power" dissipated, which is related to current and resistance. While total impedance will increase, it is due to increased reactance of the speaker at some frequencies. Because voltage and current are out of phase in a reactance, heat dissipated is not what you'd think it would be (and is quite a bit lower than in the case of a resistor).
Regardless, this effect is happening all the time to every speaker you play through, but you never notice issues result. So you need not worry about damage to the load resistors or speaker, but know only that the reflected primary impedance will be higher when the speaker's impedance increases. As noted earlier, you might minimize this effect somewhat by placing the speaker/load resistors in parallel.
And, as Sluckey pointed out, if the speaker's impedance increases, it will dissipate a little less power than when its impedance matches load resistor resistance. But you don't really care, because you were gonna select resistors rated for at least double the anticipated power for safety and cool operation, right?