Update on the sequencing of pENTR_LilrB2: It's correct. One of the middle primers did not bind, but it had bound previously, showing that that portion of the gene is fine, too. And it's in the middle of the gene.
The problem with LilrB2TCSG4 was that the last 1/4th of the gene was missing, NOT from the middle. So, yes, missing middle chunks of genes is still unlikely.
HL, hEF1a: PirBTCSG4 undigested, hEF1a: PirBTCSG4 6, 7, 8, 9, 10, TREt:YFPCofilin undigested, digested, TREt:TEVpCofilin undigested, digested
HL, LilrB2 PCR, YFP PCR.
Slightly prettier picture: