The simple answer is yes. The settlement was offered to you through your legal representative.
A lot of other poissible considerations come to mind. Do your medical providers or health insurance carrier or Medicare/Medicaid have a lien?
Why and how did your lawyer "drop" you? If you fired him/her, a lien for fees and /or costs may exist. Even if he/she quit , a lien for costs could still exist.
What I'm trying to say is that is that the simple question may not have a simple , rela world answer that protects your interest. At least consult with a lawyer.
If there is an offer on the table in your case of course you should be able to receive settlement proceeds. But, there are far too many variables, such as liens, to answer this with a simple yes or no. Slip and Fall cases are not an open and shut matter. Here's Why:
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Typically unless that offer had an expiration date or other provisions causing it to expire, it is likley you can still settle for that amount. You will need to speak with the adjuster to move settlement forward. However, it is probably in your best interest to consult with another attorney and get a 2nd opinion as to the merits of your claim. Depending on the facts of your case, it may be worth more or less than what is offered.
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This case is far from over. Retain a new lawyer, and make sure he/she is going to make sure your case is thoroughly investigated, medical conditions can go unntoiced for years, and then zap the life out of you. Get a 2nd opinion, hire another lawyer, see it through.
There are not enough facts to answer your question. For example, if you were offered $5,000, and rejected the offer by making a counter-demand of some type, then technically the $5,000 would be off the table. Furthermore, there are potentially all kinds of issue related to outstanding medical bills, liens, LOPs, etc. to know if you would actually get the funds. You really need to get into another lawyer. Since your most recent attorney "dropped" you, they will not have a charging lien for fees. This should make it easier to find a new attorney. Best of luck.
DISCLAIMER: Attorney Scott McPherson is a sole practitioner representing injured persons in the Tampa Bay area of Florida. He has extensive litigation experience in State and Federal Court, and has argued before Florida's appellate courts. Answers provided by Attorney McPherson are not to be deemed legal advice, as it would be impossible to analyze the merits of a case based on a single forum question. No attorney-client relationship is created or implied by Attorney McPherson's responses.