In order to provide safety in a borehole communicating in particular with a cavity washed out from rock salt and containing gas under pressure, the prior art provides devices suffering from the drawback of reducing the flow sections through the tubes in the borehole. The present invention minimizes this section reduction by means of a hollow cylindrical sleeve closed inside by a plug and including ducts formed in its wall in such a manner as to cross over the flows of fluid taking place respectively in a central tube of the borehole and in the annular space between the central tube and a peripheral tube. In one embodiment of the present invention, the sleeve is sandwiched between portions of the central tube and of the peripheral tube, with safety valves advantageously being mounted on the portions of central tube above and below the sleeve. This provides a safety system suitable for implementing the method of the invention by being connected in line with the central tube and the peripheral tube of the borehole. As a result, both the flow established in the central tube and the flow established in the annular space can be stopped in the event of an accident by the valves without the valves significantly reducing the normal flow section of the central tube. When exploiting a well in "dual completion" mode, this structure also provides significantly larger flow sections than provided by prior art tube systems.