This is only possible for a limited time
If we keep on taking more renewable resources than can be replenished, then eventually they will become depleted.
This has already happened locally in some places, for example the collapse of cod stocks in Newfoundland in the 1980s.
At present, people are often able to shift their sourcing when this happens – we go to a new fishing ground or forest, clear new land for farming, or target a different population or a still-common species.
But at current consumption rates, these resources will eventually run out too. Some ecosystems will collapse even before the resource is completely gone.
The consequences of excess greenhouse gases in the atmosphere are also already being seen, like climate change and ocean acidification. These place additional stresses on biodiversity and ecosystems.