Dear Student,
Here is the answer to you asked query-
The next step of the experiment will not be affected since the recombinant DNA molecule is circular and does not have any free ends. Therefore no substrate will be available for exonuclease enzyme to act and remove the nucleotides from the free ends of the given DNA. If the restriction enzyme does not cut the DNA at specific recogniton sequences than the desired gene can not be obtained as there will not sticky ends present and that specific character will also not be obtained.
Regards