The Example of Colorado Law
In Colorado, a private individual who is a victim of theft can bring a lawsuit for civil theft in which a prevailing theft victim can recover the actual economic amount of the theft (including pre-judgment interest at the statutory rate from lost use of the stolen property per a separate pre-judgment interest statute), treble damages (i.e. actual damages plus twice that amount as a civil penalty), and their attorneys' fees and the costs of the litigation.
Colorado Revised Statutes § 18-4-405. Rights in stolen property
All property obtained by theft, robbery, or burglary shall be restored
to the owner, and no sale, whether in good faith on the part of the
purchaser or not, shall divest the owner of his right to such
property. The owner may maintain an action not only against the taker
thereof but also against any person in whose possession he finds the
property. In any such action, the owner may recover two hundred
dollars or three times the amount of the actual damages sustained by
him, whichever is greater, and may also recover costs of the action
and reasonable attorney fees; but monetary damages and attorney fees
shall not be recoverable from a good-faith purchaser or good-faith
holder of the property.
Returning the property stolen doesn't change the fact that civil theft was committed, it only reduces the amount of the damages by the amount repaid and prevents interest from continuing to accrue.
In practice, it would be very uncommon for someone to bring a suit for civil theft after they are repaid. But, nothing in principle prevents this from happening until the statute of limitations runs (in Colorado that is probably three years from the date that the theft is discovered), although there might be an argument that accepting the funds returned by mutual agreement might constitute a waiver of their claim, or might give rise to equitable defenses of estoppel or laches.
Of course, in the U.S., even if the company doesn't press charges, a prosecutor does have the authority to press criminal charges without their consent. A theft victim does not have the legal authority to relieve you of criminal liability for theft. There are some countries other than the U.S. where a theft victim can relieve someone who committed theft of criminal liability (if I recall correctly, Germany is one of them), but that is a minority position internationally as a legal matter (although actual practice is often different).
Civil Lawsuits For Theft In Other Jurisdictions
While most states do not have a statutory civil theft statute, almost every state and country would allow a civil lawsuit for "conversion" or the equivalent for taking property that does not belong to you for your own benefit (which is a tort). Other U.S. states and other countries would vary over whether repayment of funds converted prior to commencement of a lawsuit limits actual damages and exemplary damages based upon actual damages to pre-judgment interest, or even constitutes a complete defense, or not.
Most U.S. states allow for an award of punitive damages in connection with an intentional tort (statutes of limitations and pre-judgment interest award rules vary greatly). Most non-U.S. jurisdictions would not allow an award of punitive damages in a civil action involving an intentional tort.
In the absence of a statutory authorization of the kind found in Colorado, attorneys' fees and costs would normally not be allowed for a U.S. plaintiff in an intentional tort case like this one, but most non-U.S. courts would allow an award of attorneys' fees and costs to a prevailing party in a case like this one.
The fact that you repaid the funds makes some defenses to future civil or criminal charges very challenging. You can't truthfully deny that you repaid the funds and that comes close to an admission of guilt. But, if you state under oath that you engaged in this conduct, you make yourself vulnerable to criminal prosecution based upon that testimony under oath.
In practice, one reason that the business is actually unlikely to sue you in this situation (unless they discovered that more than $50,000 was taken) is that having lost your job and paid them $50,000 you may not be able to pay even a large judgment if it was awarded against you (although such a judgment, if entered, would probably not be dischargeable in bankruptcy under U.S. law). So, the cost-benefit analysis of such a suit for the company might not make much sense.
Also, while having a suit like this filed against you would certainly damage your reputation seriously in a way that could be located with a public records search, it might also moderately harm the reputation of the company which revealed that its internal controls were lax enough to make it possible for the theft to happen. In the case of a large business the damage that this could do to the fair market value of the business and its creditworthiness might outweigh the benefit it would receive from bringing such a lawsuit.