If your spectral library contains peptides that you would like to add to your document, but those peptides could not have been produced by the selected enzyme, you should go to:
View > Spectral Libraries
and push the "Add All" button in the Spectral Library Explorer.

If you have created a background proteome (Settings > Peptide Settings > Digestion), then you can check the checkbox "Associate Proteins" in the Spectral Library Explorer and the peptides will be added to the correct proteins in your document even though they could not have been produced by the enzyme that you have selected.
(It would be nice if you could have used "Refine > Associate Proteins" to distribute the newly added peptides to the appropriate proteins, but, I believe the Associate Proteins dialog does insist that the peptide match the enzyme, so you have to rely on the "Associate Proteins" checkbox in the Spectral Library Explorer instead).

In terms of the peptides that you are describing where only one end of the peptide could have been cleaved by the enzyme, you can probably get Skyline to accept them by editing the enzyme definition and checking the "Allow semi-cleavage" checkbox in the Edit Enzyme dialog.
Skyline already has a built-in enzyme called "Trypsin (semi)" that you can select at "Settings > Peptide Settings > Digestion".

I hope this helps. Let us know if there is something else that you are trying to accomplish that you are unable to do so, and we might be able to come up with a workaround for you.
-- Nick

Dear Nick,
first of all thanks for your answer.

I do not have a background proteome since I only have to analyze one synthetic peptide and its modifications and very often only in full scan mode without fragmentation scans. The sequences are usually artificial anyway.

So I just need the intact mass with the different charge states plus the mass differences for the modifications and the aborted sequences.

Please find some screenshot from the peaksstudio denovo software that I can use when I have MS2 data. I hope this helps
Kind regards
Jana

You could also use the "Edit > Insert > Peptides" menu item to insert these peptides into your Skyline document.
You can explicitly list the peptide sequences which you would like added to the document. You specify the name of the protein in the "Protein Name" column in order to control how the peptides are grouped together in the Targets tree.
When you insert peptides in this way, the Protein in the Targets tree will not know what its amino acid sequence is, and the peptides will not know what their position is in the protein sequence, so things such as "Previous Aa" or "First Position" will end up being blank in the document grid.
Does that work for you?
-- Nick