For example, one possible solution.
1.
procedure TMainForm.UniFormCreate(Sender: TObject);
begin
with UniMemo1.JSInterface do
JSAddListener('blur', 'function(){ajaxRequest(this, "_blur", ["cpos="+this.inputEl.dom.selectionStart])}');
end;
2.
procedure TMainForm.UniMemo1AjaxEvent(Sender: TComponent; EventName: string;
Params: TUniStrings);
begin
if EventName = '_blur' then
(Sender as TUniMemo).CustomAttribs.Values['cpos'] := Params.Values['cpos'];
end;
3. Usage:
procedure TMainForm.UniButton1Click(Sender: TObject);
begin
ShowMessage(UniMemo1.CustomAttribs.Values['cpos'])
end;