@bkscha: Yes you could apply for F-2 during the grace period of 60 days.
G-1145, E-Notification of Application/Petition Acceptance
A cover letter (one page) requesting the change of status from your current status to F-2. This letter should include a brief explanation as why you wish to change to F-2 status. You should also provide a checklist of the documentation you are including in your application.
USCIS Form I-539 Application to Extend/Change Nonimmigrant Status, including application fee.
Evidence of financial support (i.e., bank statement, F-1's assistantship letter, etc.).
Copy of your entire F-2 I-20 (the F-1 must sign the “Student Attestation” section on page 1 of the form before making a copy). Do NOT send your original I-20. USCIS does not require the original and will not return it.
Copies of all of the immigration documents (e.g. DS-2019, I-20, I-797, paper or print-out of electronic Form I-94, valid passport, visa stamp, EAD card, etc.) showing that you are currently in lawful non-immigrant status.
Copy of the waiver (if you were previously subject to the 212(e) Two-Year Foreign Residency Requirement while in J status), if applicable.
Copies of all of your F-1 spouse's/parent's immigration documents (e.g., I-20, I-797, paper or print-out of electronic Form I-94, valid passport, visa stamp, EAD card, etc.) showing that he/she is currently in lawful F-1 status.
Proof of your relationship with your F-1 spouse/parent (e.g., copy of marriage certificate, birth certificate, passport information).
Yes, @istmaitra bro USCIS now gives 60 days grace period to find another job or change your status for H1B, this rule was passed in 2016 which states the below:
Establish a grace period of up to 60 consecutive days during each authorized validity period for certain high-skilled nonimmigrant workers when their employment ends before the end of their authorized validity period, so they may more readily pursue new employment and an extension of their nonimmigrant status.
Check this link out: