Does anyone know why any person who lives in the southern border tier of the USA would ever vote for Biden ?

 Biden has never said that.  Democrats do not want "open borders".  What they want is a more permissive immigration system.

So you're lying about Biden's plans.  But your premise, that people who have the most at stake with immigration are most opposed to it, is also faulty. In fact, just the opposite is true.  Opposition to immigration tends to be inversely correlated with how much experience a region has with immigration.  If we look at recent political results, we see that Democrats tend to be dominant in areas of the country which have relatively high levels of immigrants.  For example, they are completely dominant in California, the state with the highest number of immigrants (legal and illegal).  In contrast, Republicans tend to be dominant in areas which have fewer immigrants.  For example, in 2020, Trump's highest margins of victory were in Wyoming and West Virginia, two states not exactly know for their large immigrant populations.  If we look at the maps of the 2020 election we can see that Republicans mostly won states in the Great Plains, Mountain West, and Southeast.  These regions, for the most part, don't have lots of immigrants, legal or otherwise (Texas and Florida being notable exceptions).  Even within states we see the same pattern repeated.  Trump won Florida overall, but Democrats won the urban centers of Orlando, Miami, Tampa, Jacksonville etc, where immigrants tend to predominate.  In New York, Democratic power is concentrated in the southern part of the state around New York City, where immigrants are most heavily concentrated.  Trump's main base of support is Upstate where there are fewer immigrants.  Your notion that people along the border reject Democrats over immigration is also false.  Biden won three out of the four states which border Mexico.  He lost Texas, but did better there than any Democrat since Bill Clinton in 1996 (when Texan Ross Perot ran as a third party, siphoning votes from the Republicans).  The more granular results show that your ideas are wrong too.  Biden did well along the border in all these states, winning all of the California counties on the border and the most populous border counties in Arizona and Texas.  In the House there's only two Republicans who represent districts along the Mexican border (out of  over 10 districts which have some border territory).  Those two Republicans represent largely empty rural districts which generally see few crossings and have comparatively few illegal immigrants when compared to Democratic strongholds like El Paso or down by Brownsville.  So the reality is that the people who have the most experience with immigration, including illegal immigration, tend to be more approving of Democrats and in favor of a more permissive immigration policy (this actually runs across party lines as many Republican politicians along the border also support immigration reform).  The people who are really upset about illegal immigration, and really animated to politically oppose it, are by and large not the people who have to deal with the consequences of it.  Instead they're mostly people in the interior of the country who don't have a lot of immigrants in their neighborhoods and don't have to directly deal with the consequences of illegal immigration.  Instead of reacting off of actual personal experience of negative consequences they've endured, they are operating off of theoretical fear of negative consequences which they imagine will come with immigration and which they hope to prevent. 

Republicans are why people vote Democrat.

He didn't say that.

Vote fraud did it

Please cite your source where he said that. You can't.

"he would open the borders to anyone willing to come in with few exceptions"

No he didn't.  Nobody buys your disinformation nonsense pipsqueak.