Yhyjyk

QGIS
I have multiple lines in one layer (trench) and multiple points in another later.

I've searched the whole Internet for a plug-in which can: connect points to the nearest line, creating a new line in a new layer.

Maybe the plug-in is already there, but I couldn't find it...

What I have:

Desired output:

You can use the QGIS Python console for this. The output results as a memory layer. I'm using QGIS 2.18.28. Probably in QGIS 3 the code does not work, due to software changes.

Just paste this code into the Python console. You have to edit the code according to your layer names. In my case I have a shapefile points and a shapefile lines. You have to know the projection of your shapefiles and they have to have the same projection. Otherwise we have to do some transformation. Choose the right projection when adding the memory layer.

from PyQt4.QtCore import *
from PyQt4.QtGui import *
from qgis.core import *
from qgis.gui import *
from qgis.networkanalysis import *

# define input layer points and lines
p_lyr = QgsMapLayerRegistry.instance().mapLayersByName('points')[0] # set your point layer name here
l_lyr = QgsMapLayerRegistry.instance().mapLayersByName('lines')[0] # set your line layer name here
lines = [feature for feature in l_lyr.getFeatures()]

# set up memory layer for the closest distance line
d_lyr = QgsVectorLayer('LineString', 'normalVector', 'memory')
QgsMapLayerRegistry.instance().addMapLayer(d_lyr)
prov = d_lyr.dataProvider()

# adding three attributes (holding point_id, line_id and the distance)
prov.addAttributes( [ QgsField("point_id", QVariant.Int), QgsField("line_id", QVariant.Int), QgsField("distance",QVariant.Int)])

feat = []
for points in p_lyr.getFeatures():
 # find closest point to line
 minDistPoint = min([l.geometry().closestSegmentWithContext(QgsPoint(points.geometry().asPoint())) for l in lines])[1]
 feat = QgsFeature()
 # create line from point to minDistPoint
 line = QgsGeometry.fromPolyline([QgsPoint(points.geometry().asPoint()), QgsPoint(minDistPoint[0], minDistPoint[1])])
 feat.setGeometry(line)
 # adding point id, line id and length of the closest distance line as a feature to the memory layer
 feat.setAttributes([int(points["id"]), int(l["id"]), line.geometry().length()])
 prov.addFeatures([feat])

d_lyr.updateExtents()
d_lyr.triggerRepaint()
d_lyr.updateFields()

There is not such a plugin. And if you do not want to use python, you can combine two build-in algorithms in QGIS3

I think that this answer can solve your problem: https://gis.stackexchange.com/a/280787/7849