They are willing (or not) to give you references, make introductions, help you with your resume, etc. because they have watched and observed how you have carried yourself. And they introduce you accordingly. Will they say “S/he’s a great business leader who was just laid off from her job, might you have time to meet him/her for coffee to network?” Or “S/he’s been successful at implementing processes and accountabilities in HR and tying them to the business. Maybe she could help with your project to create HR metrics while she is looking for a full-time job?”
These types of introductions are invaluable. Have you been a good business partner? Have you offered help when someone else in need reached out? Have you introduced your network to other professionals who might aid in their success? I owe much of where I am today because of those relationships. And a little hard work helps too!
When you need a new job, will your network be willing to help you?