The Florida Bankruptcy Exemptions can be viewed by going here. As you can see in the list, two exemptions that seem potentially applicable to damages from an on-the-job accident are the "Damages to employees for injuries in hazardous occupations" exemption under Florida Statute 769.05 which you cited (see below) or the "Workers' compensation" exemption under Florida Statute 440.22.
Also, Florida allows someone who files bankruptcy in Florida to use the Federal supplemental exemptions, which can be viewed here. The Federal supplemental exemptions do have some disability-type exemptions, but they are pretty limited.
So, which, if any, of these exemptions will apply depends on the nature of the accident (i.e. Hazardous occupation or not? Government employee or not? Worker's comp income or not? etc).
The Florida Statute you cited, 769.05, can be viewed here, and says: "769.05 Proceeds of recovery for injuries exempt from garnishment and execution.--Writs of garnishment, execution or other processes, shall not issue out of any court to reach any money due or likely to become due as damages under the provisions of this chapter. "
So, it appears that 769.05 does protect damages awarded to employees for injuries in hazardous occupations in bankruptcy if those damages are awarded under Chapter 769 of the Florida Statutes, which can be viewed here.
I hope this helps and a positive feedback is always appreciated if this was useful to you.
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