overrun
To spread and take over a place in large numbers.
To overrun means to spread over or occupy an area in large numbers, like when weeds overrun a garden that hasn't been tended in weeks, or ants overrun a picnic blanket after someone spills lemonade. The word suggests something taking over a space completely, usually in an overwhelming or unwanted way.
You might hear that a fort was overrun by enemy soldiers in a history lesson, meaning the attackers swarmed over its defenses. A house might be overrun with mice, or a park might be overrun with dandelions. The word captures that sense of being overtaken by sheer numbers.
Overrun also means to go beyond a planned limit, especially with time or money. When a construction project overruns its budget, it ends up costing more than expected. When a meeting overruns, it goes past its scheduled end time. This meaning suggests spilling over a boundary that was supposed to contain something: builders had $50,000 to work with but ended up spending $65,000, or a 30-minute meeting stretched to 50 minutes.
In both meanings, something crosses a line it should have stayed behind, whether that's weeds invading where flowers should grow or expenses climbing past what was planned.