A new series of experiments has been performed to find out the conditions for the formation of a glass phase in solid 4He in the region where an anomalous behavior attributed to the supersolid effect was observed previously. A special two-chamber cell was used to deform the sample in situ. The contribution of the glass phase was identified by analyzing the measured temperature dependence of the sample pressure under different experimental conditions. It is found that the contribution of the glass phase increased sharply after deformation of the sample and practically disappears after its annealing.