Please help!

Years ago these trees called laurus nobilis was planted in my front yard. To our horror it was discovered that these trees sent out runners all over the place. From the ground the gardener pulled out this fabric called weed block and below this week block were masses of runners or suckers. Worst, some of these runners/suckers had grown up against the foundation of the house. Here are some questions that come to mind:

• Could these runners work itself underground? The runners were found to be between the weed block and the ground surface. I’m concerned about the runners that were found against the foundation of the house. And just how far down does the foundation go?
• What’s the best way to kill these runners? Will a mixture of salt and vinegar do the work? I’m trying to avoid using poisons.
• Would it not be best to just remove those trees? Some of the trees are near the concrete driveway of a neighbor.