Due to being under the cap when free agency began, they would lose their MLE.
I have a clarification.
According to
http://members.cox.net/lmcoon/salarycap.htm#Q20, ‘(f)or example, with a $49.5 million salary cap, assume it's the offseason, and a team has $41 million committed to salaries, along with a Mid-Level exception for $5 million, a Traded Player exception for $2.5 million, and an unrenounced free agent whose free agent amount is $2 million. Their salaries and exceptions total $50.5 million, or $1 million over the cap. What if their free agent signs with another team? The $2 million free agent amount comes off their cap, so their team salary drops to $48.5 million. This total is below the cap so the team loses its Mid-Level and Traded Player exceptions.;
So, even during the new season, a team could still lose its mid-level and biannual exceptions.