If an INS or IRS is switched OFF in flight, either inadvertently or in response to a checklist action, then the alignment is lost. If it subsequently becomes safe to switch it back on, you cannot get a full gyro-compassing in flight because the lateral accelerometer of the East gyro will not be able to distinguish between Earth rate and accelerations caused by movement of the aircraft. This is why the aircraft has to be stationary during ground alignment.
However, if you select ATT REF (on a typical IN) or ATT on the B737-400 IRS, either after switching OFF, or directly from NAV (following a computing, but not gyro, failure), the gyros now work as a combination of a superior form of DGI and ADI. If you have a period of steady unaccelerated flight, the gyros will erect to the vertical by sensing gravity from the accelerometers and the heading can then be set by the pilot to be the same as the heading from some other source (such as a slaved gyro compass).
Attitude information will stay good for the rest of flight, but the azimuth information is not corrected for Earth rate or Transport Wander, so whilst it will have the very low real drift rate associated with IN-quality gyros (in the order or 1/100 degree per hour), it still needs to be corrected every 20 minutes or so from another source because of the ER and TW drifts.
However, all nav computing facilities (readouts of drift, track, waypoint steering, distance to go, etc) are no longer available.