Ebbie- Hopefully the drill hole with its pipe is sufficiently deep in the rock formations that it will hold up when the 'top' is sealed.
This usually is the case.
The sediments containing the oil are covered with thousands of feet more of sedimentary beds which have been able to seal the high pressure oil horizon for lo! several million years.

Just a note for general information-
When sediments containing much organic debris (the dead small organisms that constitute the bulk of life in the oceans plus plant material, algae, etc.), are buried by suceeding layers of sediments, the heat and pressure at depth act to convert part of the organic matter into hydrocarbons; liquid and gaseous fractions forming the oil. These liquid and gaseous materials, if there is porosity in the sedimentary bed, will migrate to a higher part of the bed, and are pooled if the porosity ceases, or there is a fold (anticline) in the bed that can trap the hydrocarbons. If there is much gas, the pressure in the 'trap' may be very high.
If heat and pressure become too great for the stability of the hydrocarbons, they may become largely gaseous plus 'inert' organic matter; eventually with great pressure and heat the hydrocarbons increase in carbon content and solids are formed that are unproducible.

On the other hand, if the sediments are highly organic, but are not sufficiently buried and heated by deep burial, the organic remains are only partly converted to liquids and gases. They pool to a certain degree, and are quite oily, but the hydrocarbon will not flow. It is organic matter of this type that constitutes the hydrocarbons being mined from the tat sands of northern Alberta (and increasingly, adjacent Saskatchewan) in Canada. These materials have become the major portion of the hydrocarbons produced in Canada and the number one source of hydrocarbons used in the U. S.