Injecting the sample in a stronger solvent than the mobile phase may be detrimental for peak widths and peak shapes, especially (but not exclusively) under isocratic conditions. The injection solvent may migrate as a plug (or peak) through the column. Because the column is designed to yield a high number of plates, i.e. to minimize axial dispersion, a strong-solvent plug (shown in blue below) may remain intact along a significant fraction of the column length. The migration velocity of analyte molecules with depend on the local solvent composition. Analyte molecules (pink) at the front end of the peak (right-hand side of the figure below) migrate more slowly than the solvent peak and they are swept up again by the plug. However, analyte molecules at the rear of the solvent peak.

A strong-solvent plug may even remain until the end of the column, in which case some of the analyte may be elutes with the solvent (a phenomenon known as “breakthrough”), followed by a very long (and possibly invisibly low) tail. Under gradient conditions such a tail is swept up and yields a peak at the expected location for the analyte. Quantitative analyses are jeopardized by breakthrough.
Reversely, an injection solvent that is a weak eluent yields peak focussing, with analyte molecules being concentrated at the end of the injection zone. Thus, if at all possible such “weak” injection solvents should be used.
Guidelines for injection in LC are to use the mobile phase or, preferably, a solvent that is a weaker eluent, as injection solvent. If a strongly eluting solvent is unavoidable, the injection volume must be as small as possible. “Sandwich” injections, in which the sample plug is preceded and followed by a plug of very weak eluent (e.g. 95% water in RPLC) do not solve all problems, but they may help dilute a solvent plug more quickly.
For more information see Sections 3.5.5 and 4.3.2.
See also breakthrough of polymers.