I think you want to do this. 'Slope' was just a parameter I used to define the continuous signal.
model EventGen
Modelica.Blocks.Sources.ExpSine source(amplitude = 10, freqHz = 1, damping = 1) ;
parameter Real threshold = 1;
Real outputSignal(start = 0);
equation
der(outputSignal) = -outputSignal;
when source.y < threshold then
reinit(outputSignal,1);
end when;
end EventGen;