It is not at all uncommon for an attorney who takes a case on a contingency fee basis to require the client to cover expenses. Indeed, that is perfectly appropriate.
All of that should be set forth in an engagement letter or retainer agreement, however. The agreement should specify the percentage contingency to which the attorney will be entitled should the case result in a recovery or settlement. It should also specify the types of expenses for which you will be responsible during the course of the litigation and the basis upon which they will be charged (i.e., the per-page amounts that will be charged, say, for xeroxing, faxes, etc.).
Disclaimer: This answer does not establish an attorney-client relationship or constitute legal advice. It is for general informational purposes only.
Normally the firm will fund the overhead expenses in a personal injury suit. It depends on the financial status of you the client and the type of lawsuit. In employment suits it is much more common to require that the client put some skin in the game so to speak. Even in Personal Injury cases the cliets are always liable for the expert fees, etc.
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Disclaimer: This answer does not constitute legal advice. I am admitted in the States of New York, New Jersey and Massachusetts only and make no attempt to opine on matters of law that are not relevant to those three States. This advice is based on general principles of law that may or may not relate to your specific situation. Facts and laws change and these possible changes will affect the advice provided here. Consult an attorney in your locale before you act on any of this advice. You should not rely on this advice alone and nothing in these communications creates an attorney client relationship. The opinions expressed herein are those of the author only and the fact that he has worked as an Assistant District Attorney; State Supreme Court Clerk; Special Assistant United States Attorney (Hawaii); Assistant Cornell University Counsel or Judge Advocate, United States Marine Corps should not be relied upon to assume that these statements reflect the policy of these organizations.