Will Braces Damage my Teeth if I Can't See the Orthodontist?

If you cannot proceed forward with treatment due to the cost, I would recommend you get the braces removed ASAP. The original orthodontist who placed your braces cannot refuse to remove them due to a lack of payment of fees.  They can however, refuse to make you retainers if your account is not paid in full.  Another orthodontist (one you did not start with) may not "want" to remove them without a cost due to the work involved and potential liability. I would suggest you contact the original orthodontist and request the braces be removed.  A final option would be to call a dental school and see if they could help.

Thank you for your question.
Brackets do collect plaque and it is hard to keep teeth and gums clean when braces are on. I would recommend to remove them if they are not actively being used.
Whenever you are ready, you always can put them back on and continue straitening your teeth.

I am sorry to hear of your circumstance that you have not been able to see an orthodontist because of financial reasons.  If you truly don't have some way to financially pay for the service, you should find someone who will remove the braces at a low cost.  The braces themselves do not cause damage to the teeth, but can encourage plaque buildup because of challenges in cleaning teeth with braces.  A bigger problem could be bad tooth movement because of extended unsupervised wire pressures on the teeth.  At least have your teeth checked out ASAP to determine likely problems.