Yesterday I got an e-mail from a freelancer who said she's delayed with her work and will deliver a few days late.
Today I got a message from another freelancer whose previous gig took longer than anticipated so this piece is also going to come later than expected.
This is the correct approach as a freelancer. Stuff happens, work gets delayed, deadlines shift. All of that is fine, and there's no shame to it. Just keep the other side in the loop.