If you're pretty confident that the line segments should join up, just add a small segment from the last point to a duplicate of the first point.

You can get the first point using ST_PointN:

SELECT ST_PointN(geom, 1) FROM myCounties;

You can add that point to the line using ST_MakeLine

SELECT ST_MakeLine(geom, (SELECT ST_PointN(geom, 1) FROM myCounties)) AS newgeom FROM myCounties;

When that works the way you want, use an UPDATE / INSERT for however you want to manage the new borders.

[Hint: this would have been more appropriate to your situation if you'd posted the table schema. Please try to ask specific questions about the specific problem that you are looking for an answer for.]

If you're pretty confident that the line segments should join up, just add a small segment from the last point to a duplicate of the first point.

You can get the first point using ST_PointN:

SELECT ST_PointN(geom, 1) FROM myCounties;

You can add that point to the line using ST_MakeLine

SELECT ST_MakeLine(geom, (SELECT ST_PointN(geom, 1) FROM myCounties)) AS newgeom FROM myCounties;

When that works the way you want, use an UPDATE / INSERT for however you want to manage the new borders.

[Hint: this would have been more appropriate to your situation if you'd posted the table schema. Please try to ask specific questions about the specific problem that you are looking for an answer for.]