(See boucher's comment for the difference in LGPL and GPL.)
The GPL also doesn't require them to "[fix] bugs or make improvements give them back to [you]".
It merely requires that if they do give the binaries to someone, including you, they have to also make available the modified source to those recipients.
I'm perfectly free to take your GPL code, modify it and run it in-house, including using it in a SaaS or web offering offering, and not give anyone access to the source modifications.
The GPL also doesn't require them to "[fix] bugs or make improvements give them back to [you]".
It merely requires that if they do give the binaries to someone, including you, they have to also make available the modified source to those recipients.
I'm perfectly free to take your GPL code, modify it and run it in-house, including using it in a SaaS or web offering offering, and not give anyone access to the source modifications.