Antonio, ослабить is weaken something (most often: control, threaded connection/nut/screw, effect, etc) while ослабнуть is when someone or something "weakens itself" (including health/physical strength/condition, etc, including a currency, meaning its exchange rate, as well as all the previously mentioned when you disregard the subject of weakening -who weakens-)

США ослабили контроль над въездом иммигрантов через границу южных штатов.
Как только контроль над въездом иммигрантов ослаб, толпы гастарбайтеров заполонили штаты с ослабленным (someone has weakened it) / ослабшим (it has weakened on its own) контролем въезда.