To answer the original question: what's the worst that can happen if you feed a 555 timer too lower voltage?
Smoke! If the voltage drops below 0V, too far into negative territory, it'll smoke.
Of course you're not doing that. If the voltage is under 2V it might work, but there's no guarantee.
Another issue is the voltage will drop, as the battery discharges under load, so your circuit should work down to around 0.8V, to extract most of the energy from the battery.
It's possible to make a PWM circuit, which will work at these low voltages. A Schmitt trigger and comparator would do the job and suitable ICs are available which will work down to near 0.8V. The only trouble is they're surface mount.
Here's a schematic. I've not selected the component values, which will depend on the desired frequency and what's available. It will also need a couple of transistors to drive the motor, which will depend on how much power it uses.
http://www.ti.com/lit/ds/symlink/sn74auc1g14.pdfhttps://docs-emea.rs-online.com/webdocs/1396/0900766b81396eb3.pdfhttp://www.ti.com/lit/ds/symlink/tlv3691.pdf